Updated from wafo.stats from scipy.stats

pywafo/src/wafo/stats/__init__.py

@@ -1,12 +1,346 @@
 """
-Statistics package in WAFO Toolbox.
+==========================================
+Statistical functions (:mod:`scipy.stats`)
+==========================================
 
-    Readme               - Readme file for module STATS in WAFO Toolbox
+.. module:: scipy.stats
+
+This module contains a large number of probability distributions as
+well as a growing library of statistical functions.
+
+Each included distribution is an instance of the class rv_continous:
+For each given name the following methods are available:
+
+.. autosummary::
+   :toctree: generated/
+
+   rv_continuous
+   rv_continuous.pdf
+   rv_continuous.logpdf
+   rv_continuous.cdf
+   rv_continuous.logcdf
+   rv_continuous.sf
+   rv_continuous.logsf
+   rv_continuous.ppf
+   rv_continuous.isf
+   rv_continuous.moment
+   rv_continuous.stats
+   rv_continuous.entropy
+   rv_continuous.fit
+   rv_continuous.expect
+
+Calling the instance as a function returns a frozen pdf whose shape,
+location, and scale parameters are fixed.
+
+Similarly, each discrete distribution is an instance of the class
+rv_discrete:
+
+.. autosummary::
+   :toctree: generated/
+
+   rv_discrete
+   rv_discrete.rvs
+   rv_discrete.pmf
+   rv_discrete.logpmf
+   rv_discrete.cdf
+   rv_discrete.logcdf
+   rv_discrete.sf
+   rv_discrete.logsf
+   rv_discrete.ppf
+   rv_discrete.isf
+   rv_discrete.stats
+   rv_discrete.moment
+   rv_discrete.entropy
+   rv_discrete.expect
+
+Continuous distributions
+========================
+
+.. autosummary::
+   :toctree: generated/
+
+   alpha             -- Alpha
+   anglit            -- Anglit
+   arcsine           -- Arcsine
+   beta              -- Beta
+   betaprime         -- Beta Prime
+   bradford          -- Bradford
+   burr              -- Burr
+   cauchy            -- Cauchy
+   chi               -- Chi
+   chi2              -- Chi-squared
+   cosine            -- Cosine
+   dgamma            -- Double Gamma
+   dweibull          -- Double Weibull
+   erlang            -- Erlang
+   expon             -- Exponential
+   exponweib         -- Exponentiated Weibull
+   exponpow          -- Exponential Power
+   f                 -- F (Snecdor F)
+   fatiguelife       -- Fatigue Life (Birnbaum-Sanders)
+   fisk              -- Fisk
+   foldcauchy        -- Folded Cauchy
+   foldnorm          -- Folded Normal
+   frechet_r         -- Frechet Right Sided, Extreme Value Type II (Extreme LB) or weibull_min
+   frechet_l         -- Frechet Left Sided, Weibull_max
+   genlogistic       -- Generalized Logistic
+   genpareto         -- Generalized Pareto
+   genexpon          -- Generalized Exponential
+   genextreme        -- Generalized Extreme Value
+   gausshyper        -- Gauss Hypergeometric
+   gamma             -- Gamma
+   gengamma          -- Generalized gamma
+   genhalflogistic   -- Generalized Half Logistic
+   gilbrat           -- Gilbrat
+   gompertz          -- Gompertz (Truncated Gumbel)
+   gumbel_r          -- Right Sided Gumbel, Log-Weibull, Fisher-Tippett, Extreme Value Type I
+   gumbel_l          -- Left Sided Gumbel, etc.
+   halfcauchy        -- Half Cauchy
+   halflogistic      -- Half Logistic
+   halfnorm          -- Half Normal
+   hypsecant         -- Hyperbolic Secant
+   invgamma          -- Inverse Gamma
+   invgauss          -- Inverse Gaussian
+   invweibull        -- Inverse Weibull
+   johnsonsb         -- Johnson SB
+   johnsonsu         -- Johnson SU
+   ksone             -- Kolmogorov-Smirnov one-sided (no stats)
+   kstwobign         -- Kolmogorov-Smirnov two-sided test for Large N (no stats)
+   laplace           -- Laplace
+   logistic          -- Logistic
+   loggamma          -- Log-Gamma
+   loglaplace        -- Log-Laplace (Log Double Exponential)
+   lognorm           -- Log-Normal
+   lomax             -- Lomax (Pareto of the second kind)
+   maxwell           -- Maxwell
+   mielke            -- Mielke's Beta-Kappa
+   nakagami          -- Nakagami
+   ncx2              -- Non-central chi-squared
+   ncf               -- Non-central F
+   nct               -- Non-central Student's T
+   norm              -- Normal (Gaussian)
+   pareto            -- Pareto
+   pearson3          -- Pearson type III
+   powerlaw          -- Power-function
+   powerlognorm      -- Power log normal
+   powernorm         -- Power normal
+   rdist             -- R-distribution
+   reciprocal        -- Reciprocal
+   rayleigh          -- Rayleigh
+   rice              -- Rice
+   recipinvgauss     -- Reciprocal Inverse Gaussian
+   semicircular      -- Semicircular
+   t                 -- Student's T
+   triang            -- Triangular
+   truncexpon        -- Truncated Exponential
+   truncnorm         -- Truncated Normal
+   tukeylambda       -- Tukey-Lambda
+   uniform           -- Uniform
+   vonmises          -- Von-Mises (Circular)
+   wald              -- Wald
+   weibull_min       -- Minimum Weibull (see Frechet)
+   weibull_max       -- Maximum Weibull (see Frechet)
+   wrapcauchy        -- Wrapped Cauchy
+
+Multivariate distributions
+==========================
+
+.. autosummary::
+   :toctree: generated/
+
+   multivariate_normal   -- Multivariate normal distribution
+
+Discrete distributions
+======================
+
+.. autosummary::
+   :toctree: generated/
+
+   bernoulli         -- Bernoulli
+   binom             -- Binomial
+   boltzmann         -- Boltzmann (Truncated Discrete Exponential)
+   dlaplace          -- Discrete Laplacian
+   geom              -- Geometric
+   hypergeom         -- Hypergeometric
+   logser            -- Logarithmic (Log-Series, Series)
+   nbinom            -- Negative Binomial
+   planck            -- Planck (Discrete Exponential)
+   poisson           -- Poisson
+   randint           -- Discrete Uniform
+   skellam           -- Skellam
+   zipf              -- Zipf
+
+Statistical functions
+=====================
+
+Several of these functions have a similar version in scipy.stats.mstats
+which work for masked arrays.
+
+.. autosummary::
+   :toctree: generated/
+
+   describe          -- Descriptive statistics
+   gmean             -- Geometric mean
+   hmean             -- Harmonic mean
+   kurtosis          -- Fisher or Pearson kurtosis
+   kurtosistest      --
+   mode              -- Modal value
+   moment            -- Central moment
+   normaltest        --
+   skew              -- Skewness
+   skewtest          --
+   tmean             -- Truncated arithmetic mean
+   tvar              -- Truncated variance
+   tmin              --
+   tmax              --
+   tstd              --
+   tsem              --
+   nanmean           -- Mean, ignoring NaN values
+   nanstd            -- Standard deviation, ignoring NaN values
+   nanmedian         -- Median, ignoring NaN values
+   variation         -- Coefficient of variation
+
+.. autosummary::
+   :toctree: generated/
+
+   cumfreq           _
+   histogram2        _
+   histogram         _
+   itemfreq          _
+   percentileofscore _
+   scoreatpercentile _
+   relfreq           _
+
+.. autosummary::
+   :toctree: generated/
+
+   binned_statistic     -- Compute a binned statistic for a set of data.
+   binned_statistic_2d  -- Compute a 2-D binned statistic for a set of data.
+   binned_statistic_dd  -- Compute a d-D binned statistic for a set of data.
+
+.. autosummary::
+   :toctree: generated/
+
+   obrientransform
+   signaltonoise
+   bayes_mvs
+   sem
+   zmap
+   zscore
+
+.. autosummary::
+   :toctree: generated/
+
+   threshold
+   trimboth
+   trim1
+
+.. autosummary::
+   :toctree: generated/
+
+   f_oneway
+   pearsonr
+   spearmanr
+   pointbiserialr
+   kendalltau
+   linregress
+
+.. autosummary::
+   :toctree: generated/
+
+   ttest_1samp
+   ttest_ind
+   ttest_rel
+   kstest
+   chisquare
+   power_divergence
+   ks_2samp
+   mannwhitneyu
+   tiecorrect
+   rankdata
+   ranksums
+   wilcoxon
+   kruskal
+   friedmanchisquare
+
+.. autosummary::
+   :toctree: generated/
+
+   ansari
+   bartlett
+   levene
+   shapiro
+   anderson
+   binom_test
+   fligner
+   mood
+
+.. autosummary::
+   :toctree: generated/
+
+   boxcox
+   boxcox_normmax
+   boxcox_llf
+
+Contingency table functions
+===========================
+
+.. autosummary::
+   :toctree: generated/
+
+   chi2_contingency
+   contingency.expected_freq
+   contingency.margins
+   fisher_exact
+
+Plot-tests
+==========
+
+.. autosummary::
+   :toctree: generated/
+
+   ppcc_max
+   ppcc_plot
+   probplot
+   boxcox_normplot
+
+
+Masked statistics functions
+===========================
+
+.. toctree::
+
+   stats.mstats
+
+
+Univariate and multivariate kernel density estimation (:mod:`scipy.stats.kde`)
+==============================================================================
+
+.. autosummary::
+   :toctree: generated/
+
+   gaussian_kde
+
+For many more stat related functions install the software R and the
+interface package rpy.
 
 """
+from __future__ import division, print_function, absolute_import
 from scipy.stats import *
-from core import *
+from .core import *
-import distributions #@Reimport
+from .stats import *
-from wafo.stats.distributions import *
+from .distributions import *
+from .rv import *
+from .morestats import *
+from ._binned_statistic import *
+from .kde import gaussian_kde
+from . import mstats
+from .contingency import chi2_contingency
+from ._multivariate import *
+from . import estimation
+
+#remove vonmises_cython from __all__, I don't know why it is included
+__all__ = [s for s in dir() if not (s.startswith('_') or s.endswith('cython'))]
+#import distributions #@Reimport
+#from wafo.stats.distributions import *
 
-import estimation

pywafo/src/wafo/stats/_discrete_distns.py

@@ -0,0 +1,762 @@
+#
+# Author:  Travis Oliphant  2002-2011 with contributions from
+#          SciPy Developers 2004-2011
+#
+from __future__ import division, print_function, absolute_import
+
+from scipy import special
+from scipy.special import gammaln as gamln
+
+from numpy import floor, ceil, log, exp, sqrt, log1p, expm1, tanh, cosh, sinh
+
+import numpy as np
+import numpy.random as mtrand
+
+from ._distn_infrastructure import (
+        rv_discrete, _lazywhere, _ncx2_pdf, _ncx2_cdf)
+
+__all__ = [
+        'binom', 'bernoulli', 'nbinom', 'geom', 'hypergeom',
+        'logser', 'poisson', 'planck', 'boltzmann', 'randint',
+        'zipf', 'dlaplace', 'skellam'
+        ]
+
+
+class binom_gen(rv_discrete):
+    """A binomial discrete random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability mass function for `binom` is::
+
+       binom.pmf(k) = choose(n, k) * p**k * (1-p)**(n-k)
+
+    for ``k`` in ``{0, 1,..., n}``.
+
+    `binom` takes ``n`` and ``p`` as shape parameters.
+
+    %(example)s
+
+    """
+    def _rvs(self, n, p):
+        return mtrand.binomial(n, p, self._size)
+
+    def _argcheck(self, n, p):
+        self.b = n
+        return (n >= 0) & (p >= 0) & (p <= 1)
+
+    def _logpmf(self, x, n, p):
+        k = floor(x)
+        combiln = (gamln(n+1) - (gamln(k+1) + gamln(n-k+1)))
+        return combiln + special.xlogy(k, p) + special.xlog1py(n-k, -p)
+
+    def _pmf(self, x, n, p):
+        return exp(self._logpmf(x, n, p))
+
+    def _cdf(self, x, n, p):
+        k = floor(x)
+        vals = special.bdtr(k, n, p)
+        return vals
+
+    def _sf(self, x, n, p):
+        k = floor(x)
+        return special.bdtrc(k, n, p)
+
+    def _ppf(self, q, n, p):
+        vals = ceil(special.bdtrik(q, n, p))
+        vals1 = vals-1
+        temp = special.bdtr(vals1, n, p)
+        return np.where(temp >= q, vals1, vals)
+
+    def _stats(self, n, p):
+        q = 1.0-p
+        mu = n * p
+        var = n * p * q
+        g1 = (q-p) / sqrt(n*p*q)
+        g2 = (1.0-6*p*q)/(n*p*q)
+        return mu, var, g1, g2
+
+    def _entropy(self, n, p):
+        k = np.r_[0:n + 1]
+        vals = self._pmf(k, n, p)
+        h = -np.sum(special.xlogy(vals, vals), axis=0)
+        return h
+binom = binom_gen(name='binom')
+
+
+class bernoulli_gen(binom_gen):
+    """A Bernoulli discrete random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability mass function for `bernoulli` is::
+
+       bernoulli.pmf(k) = 1-p  if k = 0
+                        = p    if k = 1
+
+    for ``k`` in ``{0, 1}``.
+
+    `bernoulli` takes ``p`` as shape parameter.
+
+    %(example)s
+
+    """
+    def _rvs(self, p):
+        return binom_gen._rvs(self, 1, p)
+
+    def _argcheck(self, p):
+        return (p >= 0) & (p <= 1)
+
+    def _logpmf(self, x, p):
+        return binom._logpmf(x, 1, p)
+
+    def _pmf(self, x, p):
+        return binom._pmf(x, 1, p)
+
+    def _cdf(self, x, p):
+        return binom._cdf(x, 1, p)
+
+    def _sf(self, x, p):
+        return binom._sf(x, 1, p)
+
+    def _ppf(self, q, p):
+        return binom._ppf(q, 1, p)
+
+    def _stats(self, p):
+        return binom._stats(1, p)
+
+    def _entropy(self, p):
+        h = -special.xlogy(p, p) - special.xlogy(1 - p, 1 - p)
+        return h
+bernoulli = bernoulli_gen(b=1, name='bernoulli')
+
+
+class nbinom_gen(rv_discrete):
+    """A negative binomial discrete random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability mass function for `nbinom` is::
+
+         nbinom.pmf(k) = choose(k+n-1, n-1) * p**n * (1-p)**k
+
+    for ``k >= 0``.
+
+    `nbinom` takes ``n`` and ``p`` as shape parameters.
+
+    %(example)s
+
+    """
+    def _rvs(self, n, p):
+        return mtrand.negative_binomial(n, p, self._size)
+
+    def _argcheck(self, n, p):
+        return (n >= 0) & (p >= 0) & (p <= 1)
+
+    def _pmf(self, x, n, p):
+        return exp(self._logpmf(x, n, p))
+
+    def _logpmf(self, x, n, p):
+        coeff = gamln(n+x) - gamln(x+1) - gamln(n)
+        return coeff + n*log(p) + x*log1p(-p)
+
+    def _cdf(self, x, n, p):
+        k = floor(x)
+        return special.betainc(n, k+1, p)
+
+    def _sf_skip(self, x, n, p):
+        # skip because special.nbdtrc doesn't work for 0<n<1
+        k = floor(x)
+        return special.nbdtrc(k, n, p)
+
+    def _ppf(self, q, n, p):
+        vals = ceil(special.nbdtrik(q, n, p))
+        vals1 = (vals-1).clip(0.0, np.inf)
+        temp = self._cdf(vals1, n, p)
+        return np.where(temp >= q, vals1, vals)
+
+    def _stats(self, n, p):
+        Q = 1.0 / p
+        P = Q - 1.0
+        mu = n*P
+        var = n*P*Q
+        g1 = (Q+P)/sqrt(n*P*Q)
+        g2 = (1.0 + 6*P*Q) / (n*P*Q)
+        return mu, var, g1, g2
+nbinom = nbinom_gen(name='nbinom')
+
+
+class geom_gen(rv_discrete):
+    """A geometric discrete random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability mass function for `geom` is::
+
+        geom.pmf(k) = (1-p)**(k-1)*p
+
+    for ``k >= 1``.
+
+    `geom` takes ``p`` as shape parameter.
+
+    %(example)s
+
+    """
+    def _rvs(self, p):
+        return mtrand.geometric(p, size=self._size)
+
+    def _argcheck(self, p):
+        return (p <= 1) & (p >= 0)
+
+    def _pmf(self, k, p):
+        return np.power(1-p, k-1) * p
+
+    def _logpmf(self, k, p):
+        return (k-1)*log1p(-p) + log(p)
+
+    def _cdf(self, x, p):
+        k = floor(x)
+        return -expm1(log1p(-p)*k)
+
+    def _sf(self, x, p):
+        return np.exp(self._logsf(x, p))
+
+    def _logsf(self, x, p):
+        k = floor(x)
+        return k*log1p(-p)
+
+    def _ppf(self, q, p):
+        vals = ceil(log1p(-q)/log1p(-p))
+        temp = self._cdf(vals-1, p)
+        return np.where((temp >= q) & (vals > 0), vals-1, vals)
+
+    def _stats(self, p):
+        mu = 1.0/p
+        qr = 1.0-p
+        var = qr / p / p
+        g1 = (2.0-p) / sqrt(qr)
+        g2 = np.polyval([1, -6, 6], p)/(1.0-p)
+        return mu, var, g1, g2
+geom = geom_gen(a=1, name='geom', longname="A geometric")
+
+
+class hypergeom_gen(rv_discrete):
+    """A hypergeometric discrete random variable.
+
+    The hypergeometric distribution models drawing objects from a bin.
+    M is the total number of objects, n is total number of Type I objects.
+    The random variate represents the number of Type I objects in N drawn
+    without replacement from the total population.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability mass function is defined as::
+
+        pmf(k, M, n, N) = choose(n, k) * choose(M - n, N - k) / choose(M, N),
+                                       for max(0, N - (M-n)) <= k <= min(n, N)
+
+    Examples
+    --------
+    >>> from scipy.stats import hypergeom
+
+    Suppose we have a collection of 20 animals, of which 7 are dogs.  Then if
+    we want to know the probability of finding a given number of dogs if we
+    choose at random 12 of the 20 animals, we can initialize a frozen
+    distribution and plot the probability mass function:
+
+    >>> [M, n, N] = [20, 7, 12]
+    >>> rv = hypergeom(M, n, N)
+    >>> x = np.arange(0, n+1)
+    >>> pmf_dogs = rv.pmf(x)
+
+    >>> fig = plt.figure()
+    >>> ax = fig.add_subplot(111)
+    >>> ax.plot(x, pmf_dogs, 'bo')
+    >>> ax.vlines(x, 0, pmf_dogs, lw=2)
+    >>> ax.set_xlabel('# of dogs in our group of chosen animals')
+    >>> ax.set_ylabel('hypergeom PMF')
+    >>> plt.show()
+
+    Instead of using a frozen distribution we can also use `hypergeom`
+    methods directly.  To for example obtain the cumulative distribution
+    function, use:
+
+    >>> prb = hypergeom.cdf(x, M, n, N)
+
+    And to generate random numbers:
+
+    >>> R = hypergeom.rvs(M, n, N, size=10)
+
+    """
+    def _rvs(self, M, n, N):
+        return mtrand.hypergeometric(n, M-n, N, size=self._size)
+
+    def _argcheck(self, M, n, N):
+        cond = rv_discrete._argcheck(self, M, n, N)
+        cond &= (n <= M) & (N <= M)
+        self.a = max(N-(M-n), 0)
+        self.b = min(n, N)
+        return cond
+
+    def _logpmf(self, k, M, n, N):
+        tot, good = M, n
+        bad = tot - good
+        return gamln(good+1) - gamln(good-k+1) - gamln(k+1) + gamln(bad+1) \
+            - gamln(bad-N+k+1) - gamln(N-k+1) - gamln(tot+1) + gamln(tot-N+1) \
+            + gamln(N+1)
+
+    def _pmf(self, k, M, n, N):
+        # same as the following but numerically more precise
+        # return comb(good, k) * comb(bad, N-k) / comb(tot, N)
+        return exp(self._logpmf(k, M, n, N))
+
+    def _stats(self, M, n, N):
+        # tot, good, sample_size = M, n, N
+        # "wikipedia".replace('N', 'M').replace('n', 'N').replace('K', 'n')
+        M, n, N = 1.*M, 1.*n, 1.*N
+        m = M - n
+        p = n/M
+        mu = N*p
+
+        var = m*n*N*(M - N)*1.0/(M*M*(M-1))
+        g1 = (m - n)*(M-2*N) / (M-2.0) * sqrt((M-1.0) / (m*n*N*(M-N)))
+
+        g2 = M*(M+1) - 6.*N*(M-N) - 6.*n*m
+        g2 *= (M-1)*M*M
+        g2 += 6.*n*N*(M-N)*m*(5.*M-6)
+        g2 /= n * N * (M-N) * m * (M-2.) * (M-3.)
+        return mu, var, g1, g2
+
+    def _entropy(self, M, n, N):
+        k = np.r_[N - (M - n):min(n, N) + 1]
+        vals = self.pmf(k, M, n, N)
+        h = -np.sum(special.xlogy(vals, vals), axis=0)
+        return h
+
+    def _sf(self, k, M, n, N):
+        """More precise calculation, 1 - cdf doesn't cut it."""
+        # This for loop is needed because `k` can be an array. If that's the
+        # case, the sf() method makes M, n and N arrays of the same shape. We
+        # therefore unpack all inputs args, so we can do the manual
+        # integration.
+        res = []
+        for quant, tot, good, draw in zip(k, M, n, N):
+            # Manual integration over probability mass function. More accurate
+            # than integrate.quad.
+            k2 = np.arange(quant + 1, draw + 1)
+            res.append(np.sum(self._pmf(k2, tot, good, draw)))
+        return np.asarray(res)
+hypergeom = hypergeom_gen(name='hypergeom')
+
+
+# FIXME: Fails _cdfvec
+class logser_gen(rv_discrete):
+    """A Logarithmic (Log-Series, Series) discrete random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability mass function for `logser` is::
+
+        logser.pmf(k) = - p**k / (k*log(1-p))
+
+    for ``k >= 1``.
+
+    `logser` takes ``p`` as shape parameter.
+
+    %(example)s
+
+    """
+    def _rvs(self, p):
+        # looks wrong for p>0.5, too few k=1
+        # trying to use generic is worse, no k=1 at all
+        return mtrand.logseries(p, size=self._size)
+
+    def _argcheck(self, p):
+        return (p > 0) & (p < 1)
+
+    def _pmf(self, k, p):
+        return -np.power(p, k) * 1.0 / k / log1p(- p)
+
+    def _stats(self, p):
+        r = log1p(-p)
+        mu = p / (p - 1.0) / r
+        mu2p = -p / r / (p - 1.0)**2
+        var = mu2p - mu*mu
+        mu3p = -p / r * (1.0+p) / (1.0 - p)**3
+        mu3 = mu3p - 3*mu*mu2p + 2*mu**3
+        g1 = mu3 / np.power(var, 1.5)
+
+        mu4p = -p / r * (
+            1.0 / (p-1)**2 - 6*p / (p - 1)**3 + 6*p*p / (p-1)**4)
+        mu4 = mu4p - 4*mu3p*mu + 6*mu2p*mu*mu - 3*mu**4
+        g2 = mu4 / var**2 - 3.0
+        return mu, var, g1, g2
+logser = logser_gen(a=1, name='logser', longname='A logarithmic')
+
+
+class poisson_gen(rv_discrete):
+    """A Poisson discrete random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability mass function for `poisson` is::
+
+        poisson.pmf(k) = exp(-mu) * mu**k / k!
+
+    for ``k >= 0``.
+
+    `poisson` takes ``mu`` as shape parameter.
+
+    %(example)s
+
+    """
+    def _rvs(self, mu):
+        return mtrand.poisson(mu, self._size)
+
+    def _logpmf(self, k, mu):
+        Pk = k*log(mu)-gamln(k+1) - mu
+        return Pk
+
+    def _pmf(self, k, mu):
+        return exp(self._logpmf(k, mu))
+
+    def _cdf(self, x, mu):
+        k = floor(x)
+        return special.pdtr(k, mu)
+
+    def _sf(self, x, mu):
+        k = floor(x)
+        return special.pdtrc(k, mu)
+
+    def _ppf(self, q, mu):
+        vals = ceil(special.pdtrik(q, mu))
+        vals1 = vals - 1
+        temp = special.pdtr(vals1, mu)
+        return np.where((temp >= q), vals1, vals)
+
+    def _stats(self, mu):
+        var = mu
+        tmp = np.asarray(mu)
+        g1 = sqrt(1.0 / tmp)
+        g2 = 1.0 / tmp
+        return mu, var, g1, g2
+poisson = poisson_gen(name="poisson", longname='A Poisson')
+
+
+class planck_gen(rv_discrete):
+    """A Planck discrete exponential random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability mass function for `planck` is::
+
+        planck.pmf(k) = (1-exp(-lambda_))*exp(-lambda_*k)
+
+    for ``k*lambda_ >= 0``.
+
+    `planck` takes ``lambda_`` as shape parameter.
+
+    %(example)s
+
+    """
+    def _argcheck(self, lambda_):
+        if (lambda_ > 0):
+            self.a = 0
+            self.b = np.inf
+            return 1
+        elif (lambda_ < 0):
+            self.a = -np.inf
+            self.b = 0
+            return 1
+        else:
+            return 0
+
+    def _pmf(self, k, lambda_):
+        fact = -expm1(-lambda_)
+        return fact * exp(-lambda_ * k)
+
+    def _cdf(self, x, lambda_):
+        k = floor(x)
+        return - expm1(-lambda_ * (k + 1))
+
+    def _ppf(self, q, lambda_):
+        vals = ceil(-1.0/lambda_ * log1p(-q)-1)
+        vals1 = (vals-1).clip(self.a, np.inf)
+        temp = self._cdf(vals1, lambda_)
+        return np.where(temp >= q, vals1, vals)
+
+    def _stats(self, lambda_):
+        mu = 1/(exp(lambda_)-1)
+        var = exp(-lambda_)/(expm1(-lambda_))**2
+        g1 = 2*cosh(lambda_/2.0)
+        g2 = 4+2*cosh(lambda_)
+        return mu, var, g1, g2
+
+    def _entropy(self, lambda_):
+        l = lambda_
+        C = -expm1(-l)
+        return l * exp(-l) / C - log(C)
+planck = planck_gen(name='planck', longname='A discrete exponential ')
+
+
+class boltzmann_gen(rv_discrete):
+    """A Boltzmann (Truncated Discrete Exponential) random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability mass function for `boltzmann` is::
+
+        boltzmann.pmf(k) = (1-exp(-lambda_)*exp(-lambda_*k)/(1-exp(-lambda_*N))
+
+    for ``k = 0,..., N-1``.
+
+    `boltzmann` takes ``lambda_`` and ``N`` as shape parameters.
+
+    %(example)s
+
+    """
+    def _pmf(self, k, lambda_, N):
+        fact = (expm1(-lambda_))/(expm1(-lambda_*N))
+        return fact*exp(-lambda_*k)
+
+    def _cdf(self, x, lambda_, N):
+        k = floor(x)
+        return (expm1(-lambda_*(k+1)))/(expm1(-lambda_*N))
+
+    def _ppf(self, q, lambda_, N):
+        qnew = -q*(expm1(-lambda_*N))
+        vals = ceil(-1.0/lambda_ * log1p(-qnew)-1)
+        vals1 = (vals-1).clip(0.0, np.inf)
+        temp = self._cdf(vals1, lambda_, N)
+        return np.where(temp >= q, vals1, vals)
+
+    def _stats(self, lambda_, N):
+        z = exp(-lambda_)
+        zN = exp(-lambda_*N)
+        mu = z/(1.0-z)-N*zN/(1-zN)
+        var = z/(1.0-z)**2 - N*N*zN/(1-zN)**2
+        trm = (1-zN)/(1-z)
+        trm2 = (z*trm**2 - N*N*zN)
+        g1 = z*(1+z)*trm**3 - N**3*zN*(1+zN)
+        g1 = g1 / trm2**(1.5)
+        g2 = z*(1+4*z+z*z)*trm**4 - N**4 * zN*(1+4*zN+zN*zN)
+        g2 = g2 / trm2 / trm2
+        return mu, var, g1, g2
+boltzmann = boltzmann_gen(name='boltzmann',
+        longname='A truncated discrete exponential ')
+
+
+class randint_gen(rv_discrete):
+    """A uniform discrete random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability mass function for `randint` is::
+
+        randint.pmf(k) = 1./(high - low)
+
+    for ``k = low, ..., high - 1``.
+
+    `randint` takes ``low`` and ``high`` as shape parameters.
+
+    Note the difference to the numpy ``random_integers`` which
+    returns integers on a *closed* interval ``[low, high]``.
+
+    %(example)s
+
+    """
+    def _argcheck(self, low, high):
+        self.a = low
+        self.b = high - 1
+        return (high > low)
+
+    def _pmf(self, k, low, high):
+        p = np.ones_like(k) / (high - low)
+        return np.where((k >= low) & (k < high), p, 0.)
+
+    def _cdf(self, x, low, high):
+        k = floor(x)
+        return (k - low + 1.) / (high - low)
+
+    def _ppf(self, q, low, high):
+        vals = ceil(q * (high - low) + low) - 1
+        vals1 = (vals - 1).clip(low, high)
+        temp = self._cdf(vals1, low, high)
+        return np.where(temp >= q, vals1, vals)
+
+    def _stats(self, low, high):
+        m2, m1 = np.asarray(high), np.asarray(low)
+        mu = (m2 + m1 - 1.0) / 2
+        d = m2 - m1
+        var = (d*d - 1) / 12.0
+        g1 = 0.0
+        g2 = -6.0/5.0 * (d*d + 1.0) / (d*d - 1.0)
+        return mu, var, g1, g2
+
+    def _rvs(self, low, high=None):
+        """An array of *size* random integers >= ``low`` and < ``high``.
+
+        If ``high`` is ``None``, then range is >=0  and < low
+        """
+        return mtrand.randint(low, high, self._size)
+
+    def _entropy(self, low, high):
+        return log(high - low)
+randint = randint_gen(name='randint', longname='A discrete uniform '
+                      '(random integer)')
+
+
+# FIXME: problems sampling.
+class zipf_gen(rv_discrete):
+    """A Zipf discrete random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability mass function for `zipf` is::
+
+        zipf.pmf(k, a) = 1/(zeta(a) * k**a)
+
+    for ``k >= 1``.
+
+    `zipf` takes ``a`` as shape parameter.
+
+    %(example)s
+
+    """
+    def _rvs(self, a):
+        return mtrand.zipf(a, size=self._size)
+
+    def _argcheck(self, a):
+        return a > 1
+
+    def _pmf(self, k, a):
+        Pk = 1.0 / special.zeta(a, 1) / k**a
+        return Pk
+
+    def _munp(self, n, a):
+        return _lazywhere(
+            a > n + 1, (a, n),
+            lambda a, n: special.zeta(a - n, 1) / special.zeta(a, 1),
+            np.inf)
+zipf = zipf_gen(a=1, name='zipf', longname='A Zipf')
+
+
+class dlaplace_gen(rv_discrete):
+    """A  Laplacian discrete random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    The probability mass function for `dlaplace` is::
+
+        dlaplace.pmf(k) = tanh(a/2) * exp(-a*abs(k))
+
+    for ``a > 0``.
+
+    `dlaplace` takes ``a`` as shape parameter.
+
+    %(example)s
+
+    """
+    def _pmf(self, k, a):
+        return tanh(a/2.0) * exp(-a * abs(k))
+
+    def _cdf(self, x, a):
+        k = floor(x)
+        f = lambda k, a: 1.0 - exp(-a * k) / (exp(a) + 1)
+        f2 = lambda k, a: exp(a * (k+1)) / (exp(a) + 1)
+        return _lazywhere(k >= 0, (k, a), f=f, f2=f2)
+
+    def _ppf(self, q, a):
+        const = 1 + exp(a)
+        vals = ceil(np.where(q < 1.0 / (1 + exp(-a)), log(q*const) / a - 1,
+                                                      -log((1-q) * const) / a))
+        vals1 = vals - 1
+        return np.where(self._cdf(vals1, a) >= q, vals1, vals)
+
+    def _stats(self, a):
+        ea = exp(a)
+        mu2 = 2.*ea/(ea-1.)**2
+        mu4 = 2.*ea*(ea**2+10.*ea+1.) / (ea-1.)**4
+        return 0., mu2, 0., mu4/mu2**2 - 3.
+
+    def _entropy(self, a):
+        return a / sinh(a) - log(tanh(a/2.0))
+dlaplace = dlaplace_gen(a=-np.inf,
+                        name='dlaplace', longname='A discrete Laplacian')
+
+
+class skellam_gen(rv_discrete):
+    """A  Skellam discrete random variable.
+
+    %(before_notes)s
+
+    Notes
+    -----
+    Probability distribution of the difference of two correlated or
+    uncorrelated Poisson random variables.
+
+    Let k1 and k2 be two Poisson-distributed r.v. with expected values
+    lam1 and lam2. Then, ``k1 - k2`` follows a Skellam distribution with
+    parameters ``mu1 = lam1 - rho*sqrt(lam1*lam2)`` and
+    ``mu2 = lam2 - rho*sqrt(lam1*lam2)``, where rho is the correlation
+    coefficient between k1 and k2. If the two Poisson-distributed r.v.
+    are independent then ``rho = 0``.
+
+    Parameters mu1 and mu2 must be strictly positive.
+
+    For details see: http://en.wikipedia.org/wiki/Skellam_distribution
+
+    `skellam` takes ``mu1`` and ``mu2`` as shape parameters.
+
+    %(example)s
+
+    """
+    def _rvs(self, mu1, mu2):
+        n = self._size
+        return mtrand.poisson(mu1, n) - mtrand.poisson(mu2, n)
+
+    def _pmf(self, x, mu1, mu2):
+        px = np.where(x < 0,
+                _ncx2_pdf(2*mu2, 2*(1-x), 2*mu1)*2,
+                _ncx2_pdf(2*mu1, 2*(1+x), 2*mu2)*2)
+        # ncx2.pdf() returns nan's for extremely low probabilities
+        return px
+
+    def _cdf(self, x, mu1, mu2):
+        x = floor(x)
+        px = np.where(x < 0,
+                _ncx2_cdf(2*mu2, -2*x, 2*mu1),
+                1-_ncx2_cdf(2*mu1, 2*(x+1), 2*mu2))
+        return px
+
+    def _stats(self, mu1, mu2):
+        mean = mu1 - mu2
+        var = mu1 + mu2
+        g1 = mean / sqrt((var)**3)
+        g2 = 1 / var
+        return mean, var, g1, g2
+skellam = skellam_gen(a=-np.inf, name="skellam", longname='A Skellam')

pywafo/src/wafo/stats/_multivariate.py

@@ -0,0 +1,493 @@
+#
+# Author: Joris Vankerschaver 2013
+#
+from __future__ import division, print_function, absolute_import
+
+from scipy.misc import doccer
+from functools import wraps
+import numpy as np
+import scipy.linalg
+
+__all__ = ['multivariate_normal']
+
+
+_LOG_2PI = np.log(2 * np.pi)
+
+
+def _process_parameters(dim, mean, cov):
+    """
+    Infer dimensionality from mean or covariance matrix, ensure that
+    mean and covariance are full vector resp. matrix.
+
+    """
+
+    # Try to infer dimensionality
+    if dim is None:
+        if mean is None:
+            if cov is None:
+                dim = 1
+            else:
+                cov = np.asarray(cov, dtype=float)
+                if cov.ndim < 2:
+                    dim = 1
+                else:
+                    dim = cov.shape[0]
+        else:
+            mean = np.asarray(mean, dtype=float)
+            dim = mean.size
+    else:
+        if not np.isscalar(dim):
+            raise ValueError("Dimension of random variable must be a scalar.")
+
+    # Check input sizes and return full arrays for mean and cov if necessary
+    if mean is None:
+        mean = np.zeros(dim)
+    mean = np.asarray(mean, dtype=float)
+
+    if cov is None:
+        cov = 1.0
+    cov = np.asarray(cov, dtype=float)
+
+    if dim == 1:
+        mean.shape = (1,)
+        cov.shape = (1, 1)
+
+    if mean.ndim != 1 or mean.shape[0] != dim:
+        raise ValueError("Array 'mean' must be vector of length %d." % dim)
+    if cov.ndim == 0:
+        cov = cov * np.eye(dim)
+    elif cov.ndim == 1:
+        cov = np.diag(cov)
+    else:
+        if cov.shape != (dim, dim):
+            raise ValueError("Array 'cov' must be at most two-dimensional,"
+                                 " but cov.ndim = %d" % cov.ndim)
+
+    return dim, mean, cov
+
+
+def _process_quantiles(x, dim):
+    """
+    Adjust quantiles array so that last axis labels the components of
+    each data point.
+
+    """
+    x = np.asarray(x, dtype=float)
+
+    if x.ndim == 0:
+        x = x[np.newaxis]
+    elif x.ndim == 1:
+        if dim == 1:
+            x = x[:, np.newaxis]
+        else:
+            x = x[np.newaxis, :]
+
+    return x
+
+
+def _squeeze_output(out):
+    """
+    Remove single-dimensional entries from array and convert to scalar,
+    if necessary.
+
+    """
+    out = out.squeeze()
+    if out.ndim == 0:
+        out = out[()]
+    return out
+
+
+def _pinv_1d(v, eps=1e-5):
+    """
+    A helper function for computing the pseudoinverse.
+
+    Parameters
+    ----------
+    v : iterable of numbers
+        This may be thought of as a vector of eigenvalues or singular values.
+    eps : float
+        Elements of v smaller than eps are considered negligible.
+
+    Returns
+    -------
+    v_pinv : 1d float ndarray
+        A vector of pseudo-inverted numbers.
+
+    """
+    return np.array([0 if abs(x) < eps else 1/x for x in v], dtype=float)
+
+
+def _psd_pinv_decomposed_log_pdet(mat, cond=None, rcond=None,
+                                  lower=True, check_finite=True):
+    """
+    Compute a decomposition of the pseudo-inverse and the logarithm of
+    the pseudo-determinant of a symmetric positive semi-definite
+    matrix.
+
+    The pseudo-determinant of a matrix is defined as the product of
+    the non-zero eigenvalues, and coincides with the usual determinant
+    for a full matrix.
+
+    Parameters
+    ----------
+    mat : array_like
+        Input array of shape (`m`, `n`)
+    cond, rcond : float or None
+        Cutoff for 'small' singular values.
+        Eigenvalues smaller than ``rcond*largest_eigenvalue``
+        are considered zero.
+        If None or -1, suitable machine precision is used.
+    lower : bool, optional
+        Whether the pertinent array data is taken from the lower or upper
+        triangle of `mat`. (Default: lower)
+    check_finite : boolean, optional
+        Whether to check that the input matrix contains only finite numbers.
+        Disabling may give a performance gain, but may result in problems
+        (crashes, non-termination) if the inputs do contain infinities or NaNs.
+
+    Returns
+    -------
+    M : array_like
+        The pseudo-inverse of the input matrix is np.dot(M, M.T).
+    log_pdet : float
+        Logarithm of the pseudo-determinant of the matrix.
+
+    """
+    # Compute the symmetric eigendecomposition.
+    # The input covariance matrix is required to be real symmetric
+    # and positive semidefinite which implies that its eigenvalues
+    # are all real and non-negative,
+    # but clip them anyway to avoid numerical issues.
+
+    # TODO: the code to set cond/rcond is identical to that in
+    # scipy.linalg.{pinvh, pinv2} and if/when this function is subsumed
+    # into scipy.linalg it should probably be shared between all of
+    # these routines.
+
+    # Note that eigh takes care of array conversion, chkfinite,
+    # and assertion that the matrix is square.
+    s, u = scipy.linalg.eigh(mat, lower=lower, check_finite=check_finite)
+
+    if rcond is not None:
+        cond = rcond
+    if cond in [None, -1]:
+        t = u.dtype.char.lower()
+        factor = {'f': 1E3, 'd': 1E6}
+        cond = factor[t] * np.finfo(t).eps
+    eps = cond * np.max(abs(s))
+
+    if np.min(s) < -eps:
+        raise ValueError('the covariance matrix must be positive semidefinite')
+
+    s_pinv = _pinv_1d(s, eps)
+    U = np.multiply(u, np.sqrt(s_pinv))
+    log_pdet = np.sum(np.log(s[s > eps]))
+
+    return U, log_pdet
+
+
+_doc_default_callparams = \
+"""mean : array_like, optional
+    Mean of the distribution (default zero)
+cov : array_like, optional
+    Covariance matrix of the distribution (default one)
+"""
+
+_doc_callparams_note = \
+"""Setting the parameter `mean` to `None` is equivalent to having `mean`
+be the zero-vector. The parameter `cov` can be a scalar, in which case
+the covariance matrix is the identity times that value, a vector of
+diagonal entries for the covariance matrix, or a two-dimensional
+array_like.
+"""
+
+_doc_frozen_callparams = ""
+
+_doc_frozen_callparams_note = \
+"""See class definition for a detailed description of parameters."""
+
+docdict_params = {
+    '_doc_default_callparams': _doc_default_callparams,
+    '_doc_callparams_note': _doc_callparams_note
+}
+
+docdict_noparams = {
+    '_doc_default_callparams': _doc_frozen_callparams,
+    '_doc_callparams_note': _doc_frozen_callparams_note
+}
+
+
+class multivariate_normal_gen(object):
+    r"""
+    A multivariate normal random variable.
+
+    The `mean` keyword specifies the mean. The `cov` keyword specifies the
+    covariance matrix.
+
+    .. versionadded:: 0.14.0
+
+    Methods
+    -------
+    pdf(x, mean=None, cov=1)
+        Probability density function.
+    logpdf(x, mean=None, cov=1)
+        Log of the probability density function.
+    rvs(mean=None, cov=1)
+        Draw random samples from a multivariate normal distribution.
+    entropy()
+        Compute the differential entropy of the multivariate normal.
+
+    Parameters
+    ----------
+    x : array_like
+        Quantiles, with the last axis of `x` denoting the components.
+    %(_doc_default_callparams)s
+
+    Alternatively, the object may be called (as a function) to fix the mean
+    and covariance parameters, returning a "frozen" multivariate normal
+    random variable:
+
+    rv = multivariate_normal(mean=None, scale=1)
+        - Frozen  object with the same methods but holding the given
+          mean and covariance fixed.
+
+    Notes
+    -----
+    %(_doc_callparams_note)s
+
+    The covariance matrix `cov` must be a (symmetric) positive
+    semi-definite matrix. The determinant and inverse of `cov` are computed
+    as the pseudo-determinant and pseudo-inverse, respectively, so
+    that `cov` does not need to have full rank.
+
+    The probability density function for `multivariate_normal` is
+
+    .. math::
+
+        f(x) = \frac{1}{\sqrt{(2 \pi)^k \det \Sigma}} \exp\left( -\frac{1}{2} (x - \mu)^T \Sigma^{-1} (x - \mu) \right),
+
+    where :math:`\mu` is the mean, :math:`\Sigma` the covariance matrix,
+    and :math:`k` is the dimension of the space where :math:`x` takes values.
+
+    Examples
+    --------
+    >>> from scipy.stats import multivariate_normal
+    >>> x = np.linspace(0, 5, 10, endpoint=False)
+    >>> y = multivariate_normal.pdf(x, mean=2.5, cov=0.5); y
+    array([ 0.00108914,  0.01033349,  0.05946514,  0.20755375,  0.43939129,
+            0.56418958,  0.43939129,  0.20755375,  0.05946514,  0.01033349])
+    >>> plt.plot(x, y)
+
+    The input quantiles can be any shape of array, as long as the last
+    axis labels the components.  This allows us for instance to
+    display the frozen pdf for a non-isotropic random variable in 2D as
+    follows:
+
+    >>> x, y = np.mgrid[-1:1:.01, -1:1:.01]
+    >>> pos = np.empty(x.shape + (2,))
+    >>> pos[:, :, 0] = x; pos[:, :, 1] = y
+    >>> rv = multivariate_normal([0.5, -0.2], [[2.0, 0.3], [0.3, 0.5]])
+    >>> plt.contourf(x, y, rv.pdf(pos))
+
+    """
+
+    def __init__(self):
+        self.__doc__ = doccer.docformat(self.__doc__, docdict_params)
+
+    def __call__(self, mean=None, cov=1):
+        """
+        Create a frozen multivariate normal distribution.
+
+        See `multivariate_normal_frozen` for more information.
+
+        """
+        return multivariate_normal_frozen(mean, cov)
+
+    def _logpdf(self, x, mean, prec_U, log_det_cov):
+        """
+        Parameters
+        ----------
+        x : ndarray
+            Points at which to evaluate the log of the probability
+            density function
+        mean : ndarray
+            Mean of the distribution
+        prec_U : ndarray
+            A decomposition such that np.dot(prec_U, prec_U.T)
+            is the precision matrix, i.e. inverse of the covariance matrix.
+        log_det_cov : float
+            Logarithm of the determinant of the covariance matrix
+
+        Notes
+        -----
+        As this function does no argument checking, it should not be
+        called directly; use 'logpdf' instead.
+
+        """
+        dim = x.shape[-1]
+        dev = x - mean
+        maha = np.sum(np.square(np.dot(dev, prec_U)), axis=-1)
+        return -0.5 * (dim * _LOG_2PI + log_det_cov + maha)
+
+    def logpdf(self, x, mean, cov):
+        """
+        Log of the multivariate normal probability density function.
+
+        Parameters
+        ----------
+        x : array_like
+            Quantiles, with the last axis of `x` denoting the components.
+        %(_doc_default_callparams)s
+
+        Notes
+        -----
+        %(_doc_callparams_note)s
+
+        Returns
+        -------
+        pdf : ndarray
+            Log of the probability density function evaluated at `x`
+
+        """
+        dim, mean, cov = _process_parameters(None, mean, cov)
+        x = _process_quantiles(x, dim)
+        prec_U, log_det_cov = _psd_pinv_decomposed_log_pdet(cov)
+        out = self._logpdf(x, mean, prec_U, log_det_cov)
+        return _squeeze_output(out)
+
+    def pdf(self, x, mean, cov):
+        """
+        Multivariate normal probability density function.
+
+        Parameters
+        ----------
+        x : array_like
+            Quantiles, with the last axis of `x` denoting the components.
+        %(_doc_default_callparams)s
+
+        Notes
+        -----
+        %(_doc_callparams_note)s
+
+        Returns
+        -------
+        pdf : ndarray
+            Probability density function evaluated at `x`
+
+        """
+        dim, mean, cov = _process_parameters(None, mean, cov)
+        x = _process_quantiles(x, dim)
+        prec_U, log_det_cov = _psd_pinv_decomposed_log_pdet(cov)
+        out = np.exp(self._logpdf(x, mean, prec_U, log_det_cov))
+        return _squeeze_output(out)
+
+    def rvs(self, mean=None, cov=1, size=1):
+        """
+        Draw random samples from a multivariate normal distribution.
+
+        Parameters
+        ----------
+        %(_doc_default_callparams)s
+        size : integer, optional
+            Number of samples to draw (default 1).
+
+        Notes
+        -----
+        %(_doc_callparams_note)s
+
+        Returns
+        -------
+        rvs : ndarray or scalar
+            Random variates of size (`size`, `N`), where `N` is the
+            dimension of the random variable.
+
+        """
+        dim, mean, cov = _process_parameters(None, mean, cov)
+        out = np.random.multivariate_normal(mean, cov, size)
+        return _squeeze_output(out)
+
+    def entropy(self, mean=None, cov=1):
+        """
+        Compute the differential entropy of the multivariate normal.
+
+        Parameters
+        ----------
+        %(_doc_default_callparams)s
+
+        Notes
+        -----
+        %(_doc_callparams_note)s
+
+        Returns
+        -------
+        h : scalar
+            Entropy of the multivariate normal distribution
+
+        """
+        dim, mean, cov = _process_parameters(None, mean, cov)
+        return 1/2 * np.log(np.linalg.det(2 * np.pi * np.e * cov))
+
+multivariate_normal = multivariate_normal_gen()
+
+
+class multivariate_normal_frozen(object):
+    def __init__(self, mean=None, cov=1):
+        """
+        Create a frozen multivariate normal distribution.
+
+        Parameters
+        ----------
+        mean : array_like, optional
+            Mean of the distribution (default zero)
+        cov : array_like, optional
+            Covariance matrix of the distribution (default one)
+
+        Examples
+        --------
+        When called with the default parameters, this will create a 1D random
+        variable with mean 0 and covariance 1:
+
+        >>> from scipy.stats import multivariate_normal
+        >>> r = multivariate_normal()
+        >>> r.mean
+        array([ 0.])
+        >>> r.cov
+        array([[1.]])
+
+        """
+        self.dim, self.mean, self.cov = _process_parameters(None, mean, cov)
+        self.prec_U, self._log_det_cov = _psd_pinv_decomposed_log_pdet(self.cov)
+
+        self._mnorm = multivariate_normal_gen()
+
+    def logpdf(self, x):
+        x = _process_quantiles(x, self.dim)
+        out = self._mnorm._logpdf(x, self.mean, self.prec_U, self._log_det_cov)
+        return _squeeze_output(out)
+
+    def pdf(self, x):
+        return np.exp(self.logpdf(x))
+
+    def rvs(self, size=1):
+        return self._mnorm.rvs(self.mean, self.cov, size)
+
+    def entropy(self):
+        """
+        Computes the differential entropy of the multivariate normal.
+
+        Returns
+        -------
+        h : scalar
+            Entropy of the multivariate normal distribution
+
+        """
+        return 1/2 * (self.dim * (_LOG_2PI + 1) + self._log_det_cov)
+
+
+# Set frozen generator docstrings from corresponding docstrings in
+# multivariate_normal_gen and fill in default strings in class docstrings
+for name in ['logpdf', 'pdf', 'rvs']:
+    method = multivariate_normal_gen.__dict__[name]
+    method_frozen = multivariate_normal_frozen.__dict__[name]
+    method_frozen.__doc__ = doccer.docformat(method.__doc__, docdict_noparams)
+    method.__doc__ = doccer.docformat(method.__doc__, docdict_params)

pywafo/src/wafo/stats/_tukeylambda_stats.py

@@ -0,0 +1,201 @@
+from __future__ import division, print_function, absolute_import
+
+import numpy as np
+from numpy import poly1d
+from scipy.special import beta
+
+
+# The following code was used to generate the Pade coefficients for the
+# Tukey Lambda variance function.  Version 0.17 of mpmath was used.
+#---------------------------------------------------------------------------
+# import mpmath as mp
+#
+# mp.mp.dps = 60
+#
+# one   = mp.mpf(1)
+# two   = mp.mpf(2)
+#
+# def mpvar(lam):
+#     if lam == 0:
+#         v = mp.pi**2 / three
+#     else:
+#         v = (two / lam**2) * (one / (one + two*lam) -
+#                               mp.beta(lam + one, lam + one))
+#     return v
+#
+# t = mp.taylor(mpvar, 0, 8)
+# p, q = mp.pade(t, 4, 4)
+# print "p =", [mp.fp.mpf(c) for c in p]
+# print "q =", [mp.fp.mpf(c) for c in q]
+#---------------------------------------------------------------------------
+
+# Pade coefficients for the Tukey Lambda variance function.
+_tukeylambda_var_pc = [3.289868133696453, 0.7306125098871127,
+                       -0.5370742306855439, 0.17292046290190008,
+                       -0.02371146284628187]
+_tukeylambda_var_qc = [1.0, 3.683605511659861, 4.184152498888124,
+                       1.7660926747377275, 0.2643989311168465]
+
+# numpy.poly1d instances for the numerator and denominator of the
+# Pade approximation to the Tukey Lambda variance.
+_tukeylambda_var_p = poly1d(_tukeylambda_var_pc[::-1])
+_tukeylambda_var_q = poly1d(_tukeylambda_var_qc[::-1])
+
+
+def tukeylambda_variance(lam):
+    """Variance of the Tukey Lambda distribution.
+
+    Parameters
+    ----------
+    lam : array_like
+        The lambda values at which to compute the variance.
+
+    Returns
+    -------
+    v : ndarray
+        The variance.  For lam < -0.5, the variance is not defined, so
+        np.nan is returned.  For lam = 0.5, np.inf is returned.
+
+    Notes
+    -----
+    In an interval around lambda=0, this function uses the [4,4] Pade
+    approximation to compute the variance.  Otherwise it uses the standard
+    formula (http://en.wikipedia.org/wiki/Tukey_lambda_distribution).  The
+    Pade approximation is used because the standard formula has a removable
+    discontinuity at lambda = 0, and does not produce accurate numerical
+    results near lambda = 0.
+    """
+    lam = np.asarray(lam)
+    shp = lam.shape
+    lam = np.atleast_1d(lam).astype(np.float64)
+
+    # For absolute values of lam less than threshold, use the Pade
+    # approximation.
+    threshold = 0.075
+
+    # Play games with masks to implement the conditional evaluation of
+    # the distribution.
+    # lambda < -0.5:  var = nan
+    low_mask = lam < -0.5
+    # lambda == -0.5: var = inf
+    neghalf_mask = lam == -0.5
+    # abs(lambda) < threshold:  use Pade approximation
+    small_mask = np.abs(lam) < threshold
+    # else the "regular" case:  use the explicit formula.
+    reg_mask = ~(low_mask | neghalf_mask | small_mask)
+
+    # Get the 'lam' values for the cases where they are needed.
+    small = lam[small_mask]
+    reg = lam[reg_mask]
+
+    # Compute the function for each case.
+    v = np.empty_like(lam)
+    v[low_mask] = np.nan
+    v[neghalf_mask] = np.inf
+    if small.size > 0:
+        # Use the Pade approximation near lambda = 0.
+        v[small_mask] = _tukeylambda_var_p(small) / _tukeylambda_var_q(small)
+    if reg.size > 0:
+        v[reg_mask] = (2.0 / reg**2) * (1.0 / (1.0 + 2 * reg) -
+                                      beta(reg + 1, reg + 1))
+    v.shape = shp
+    return v
+
+
+# The following code was used to generate the Pade coefficients for the
+# Tukey Lambda kurtosis function.  Version 0.17 of mpmath was used.
+#---------------------------------------------------------------------------
+# import mpmath as mp
+#
+# mp.mp.dps = 60
+#
+# one   = mp.mpf(1)
+# two   = mp.mpf(2)
+# three = mp.mpf(3)
+# four  = mp.mpf(4)
+#
+# def mpkurt(lam):
+#     if lam == 0:
+#         k = mp.mpf(6)/5
+#     else:
+#         numer = (one/(four*lam+one) - four*mp.beta(three*lam+one, lam+one) +
+#                  three*mp.beta(two*lam+one, two*lam+one))
+#         denom = two*(one/(two*lam+one) - mp.beta(lam+one,lam+one))**2
+#         k = numer / denom - three
+#     return k
+#
+# # There is a bug in mpmath 0.17: when we use the 'method' keyword of the
+# # taylor function and we request a degree 9 Taylor polynomial, we actually
+# # get degree 8.
+# t = mp.taylor(mpkurt, 0, 9, method='quad', radius=0.01)
+# t = [mp.chop(c, tol=1e-15) for c in t]
+# p, q = mp.pade(t, 4, 4)
+# print "p =", [mp.fp.mpf(c) for c in p]
+# print "q =", [mp.fp.mpf(c) for c in q]
+#---------------------------------------------------------------------------
+
+# Pade coefficients for the Tukey Lambda kurtosis function.
+_tukeylambda_kurt_pc = [1.2, -5.853465139719495, -22.653447381131077,
+                        0.20601184383406815, 4.59796302262789]
+_tukeylambda_kurt_qc = [1.0, 7.171149192233599, 12.96663094361842,
+                        0.43075235247853005, -2.789746758009912]
+
+# numpy.poly1d instances for the numerator and denominator of the
+# Pade approximation to the Tukey Lambda kurtosis.
+_tukeylambda_kurt_p = poly1d(_tukeylambda_kurt_pc[::-1])
+_tukeylambda_kurt_q = poly1d(_tukeylambda_kurt_qc[::-1])
+
+
+def tukeylambda_kurtosis(lam):
+    """Kurtosis of the Tukey Lambda distribution.
+
+    Parameters
+    ----------
+    lam : array_like
+        The lambda values at which to compute the variance.
+
+    Returns
+    -------
+    v : ndarray
+        The variance.  For lam < -0.25, the variance is not defined, so
+        np.nan is returned.  For lam = 0.25, np.inf is returned.
+
+    """
+    lam = np.asarray(lam)
+    shp = lam.shape
+    lam = np.atleast_1d(lam).astype(np.float64)
+
+    # For absolute values of lam less than threshold, use the Pade
+    # approximation.
+    threshold = 0.055
+
+    # Use masks to implement the conditional evaluation of the kurtosis.
+    # lambda < -0.25:  kurtosis = nan
+    low_mask = lam < -0.25
+    # lambda == -0.25: kurtosis = inf
+    negqrtr_mask = lam == -0.25
+    # lambda near 0:  use Pade approximation
+    small_mask = np.abs(lam) < threshold
+    # else the "regular" case:  use the explicit formula.
+    reg_mask = ~(low_mask | negqrtr_mask | small_mask)
+
+    # Get the 'lam' values for the cases where they are needed.
+    small = lam[small_mask]
+    reg = lam[reg_mask]
+
+    # Compute the function for each case.
+    k = np.empty_like(lam)
+    k[low_mask] = np.nan
+    k[negqrtr_mask] = np.inf
+    if small.size > 0:
+        k[small_mask] = _tukeylambda_kurt_p(small) / _tukeylambda_kurt_q(small)
+    if reg.size > 0:
+        numer = (1.0 / (4 * reg + 1) - 4 * beta(3 * reg + 1, reg + 1) +
+                 3 * beta(2 * reg + 1, 2 * reg + 1))
+        denom = 2 * (1.0/(2 * reg + 1) - beta(reg + 1, reg + 1))**2
+        k[reg_mask] = numer / denom - 3
+
+    # The return value will be a numpy array; resetting the shape ensures that
+    # if `lam` was a scalar, the return value is a 0-d array.
+    k.shape = shp
+    return k

pywafo/src/wafo/stats/contingency.py

@@ -0,0 +1,271 @@
+"""Some functions for working with contingency tables (i.e. cross tabulations).
+"""
+
+
+from __future__ import division, print_function, absolute_import
+
+from functools import reduce
+import numpy as np
+from .stats import power_divergence
+
+
+__all__ = ['margins', 'expected_freq', 'chi2_contingency']
+
+
+def margins(a):
+    """Return a list of the marginal sums of the array `a`.
+
+    Parameters
+    ----------
+    a : ndarray
+        The array for which to compute the marginal sums.
+
+    Returns
+    -------
+    margsums : list of ndarrays
+        A list of length `a.ndim`.  `margsums[k]` is the result
+        of summing `a` over all axes except `k`; it has the same
+        number of dimensions as `a`, but the length of each axis
+        except axis `k` will be 1.
+
+    Examples
+    --------
+    >>> a = np.arange(12).reshape(2, 6)
+    >>> a
+    array([[ 0,  1,  2,  3,  4,  5],
+           [ 6,  7,  8,  9, 10, 11]])
+    >>> m0, m1 = margins(a)
+    >>> m0
+    array([[15],
+           [51]])
+    >>> m1
+    array([[ 6,  8, 10, 12, 14, 16]])
+
+    >>> b = np.arange(24).reshape(2,3,4)
+    >>> m0, m1, m2 = margins(b)
+    >>> m0
+    array([[[ 66]],
+           [[210]]])
+    >>> m1
+    array([[[ 60],
+            [ 92],
+            [124]]])
+    >>> m2
+    array([[[60, 66, 72, 78]]])
+    """
+    margsums = []
+    ranged = list(range(a.ndim))
+    for k in ranged:
+        marg = np.apply_over_axes(np.sum, a, [j for j in ranged if j != k])
+        margsums.append(marg)
+    return margsums
+
+
+def expected_freq(observed):
+    """
+    Compute the expected frequencies from a contingency table.
+
+    Given an n-dimensional contingency table of observed frequencies,
+    compute the expected frequencies for the table based on the marginal
+    sums under the assumption that the groups associated with each
+    dimension are independent.
+
+    Parameters
+    ----------
+    observed : array_like
+        The table of observed frequencies.  (While this function can handle
+        a 1-D array, that case is trivial.  Generally `observed` is at
+        least 2-D.)
+
+    Returns
+    -------
+    expected : ndarray of float64
+        The expected frequencies, based on the marginal sums of the table.
+        Same shape as `observed`.
+
+    Examples
+    --------
+    >>> observed = np.array([[10, 10, 20],[20, 20, 20]])
+    >>> expected_freq(observed)
+    array([[ 12.,  12.,  16.],
+           [ 18.,  18.,  24.]])
+
+    """
+    # Typically `observed` is an integer array. If `observed` has a large
+    # number of dimensions or holds large values, some of the following
+    # computations may overflow, so we first switch to floating point.
+    observed = np.asarray(observed, dtype=np.float64)
+
+    # Create a list of the marginal sums.
+    margsums = margins(observed)
+
+    # Create the array of expected frequencies.  The shapes of the
+    # marginal sums returned by apply_over_axes() are just what we
+    # need for broadcasting in the following product.
+    d = observed.ndim
+    expected = reduce(np.multiply, margsums) / observed.sum() ** (d - 1)
+    return expected
+
+
+def chi2_contingency(observed, correction=True, lambda_=None):
+    """Chi-square test of independence of variables in a contingency table.
+
+    This function computes the chi-square statistic and p-value for the
+    hypothesis test of independence of the observed frequencies in the
+    contingency table [1]_ `observed`.  The expected frequencies are computed
+    based on the marginal sums under the assumption of independence; see
+    `scipy.stats.contingency.expected_freq`.  The number of degrees of
+    freedom is (expressed using numpy functions and attributes)::
+
+        dof = observed.size - sum(observed.shape) + observed.ndim - 1
+
+
+    Parameters
+    ----------
+    observed : array_like
+        The contingency table. The table contains the observed frequencies
+        (i.e. number of occurrences) in each category.  In the two-dimensional
+        case, the table is often described as an "R x C table".
+    correction : bool, optional
+        If True, *and* the degrees of freedom is 1, apply Yates' correction
+        for continuity.  The effect of the correction is to adjust each
+        observed value by 0.5 towards the corresponding expected value.
+    lambda_ : float or str, optional.
+        By default, the statistic computed in this test is Pearson's
+        chi-squared statistic [2]_.  `lambda_` allows a statistic from the
+        Cressie-Read power divergence family [3]_ to be used instead.  See
+        `power_divergence` for details.
+
+    Returns
+    -------
+    chi2 : float
+        The test statistic.
+    p : float
+        The p-value of the test
+    dof : int
+        Degrees of freedom
+    expected : ndarray, same shape as `observed`
+        The expected frequencies, based on the marginal sums of the table.
+
+    See Also
+    --------
+    contingency.expected_freq
+    fisher_exact
+    chisquare
+    power_divergence
+
+    Notes
+    -----
+    An often quoted guideline for the validity of this calculation is that
+    the test should be used only if the observed and expected frequency in
+    each cell is at least 5.
+
+    This is a test for the independence of different categories of a
+    population. The test is only meaningful when the dimension of
+    `observed` is two or more.  Applying the test to a one-dimensional
+    table will always result in `expected` equal to `observed` and a
+    chi-square statistic equal to 0.
+
+    This function does not handle masked arrays, because the calculation
+    does not make sense with missing values.
+
+    Like stats.chisquare, this function computes a chi-square statistic;
+    the convenience this function provides is to figure out the expected
+    frequencies and degrees of freedom from the given contingency table.
+    If these were already known, and if the Yates' correction was not
+    required, one could use stats.chisquare.  That is, if one calls::
+
+        chi2, p, dof, ex = chi2_contingency(obs, correction=False)
+
+    then the following is true::
+
+        (chi2, p) == stats.chisquare(obs.ravel(), f_exp=ex.ravel(),
+                                     ddof=obs.size - 1 - dof)
+
+    The `lambda_` argument was added in version 0.13.0 of scipy.
+
+    References
+    ----------
+    .. [1] "Contingency table", http://en.wikipedia.org/wiki/Contingency_table
+    .. [2] "Pearson's chi-squared test",
+           http://en.wikipedia.org/wiki/Pearson%27s_chi-squared_test
+    .. [3] Cressie, N. and Read, T. R. C., "Multinomial Goodness-of-Fit
+           Tests", J. Royal Stat. Soc. Series B, Vol. 46, No. 3 (1984),
+           pp. 440-464.
+
+    Examples
+    --------
+    A two-way example (2 x 3):
+
+    >>> obs = np.array([[10, 10, 20], [20, 20, 20]])
+    >>> chi2_contingency(obs)
+    (2.7777777777777777,
+     0.24935220877729619,
+     2,
+     array([[ 12.,  12.,  16.],
+            [ 18.,  18.,  24.]]))
+
+    Perform the test using the log-likelihood ratio (i.e. the "G-test")
+    instead of Pearson's chi-squared statistic.
+
+    >>> g, p, dof, expctd = chi2_contingency(obs, lambda_="log-likelihood")
+    >>> g, p
+    (2.7688587616781319, 0.25046668010954165)
+
+    A four-way example (2 x 2 x 2 x 2):
+
+    >>> obs = np.array(
+    ...     [[[[12, 17],
+    ...        [11, 16]],
+    ...       [[11, 12],
+    ...        [15, 16]]],
+    ...      [[[23, 15],
+    ...        [30, 22]],
+    ...       [[14, 17],
+    ...        [15, 16]]]])
+    >>> chi2_contingency(obs)
+    (8.7584514426741897,
+     0.64417725029295503,
+     11,
+     array([[[[ 14.15462386,  14.15462386],
+              [ 16.49423111,  16.49423111]],
+             [[ 11.2461395 ,  11.2461395 ],
+              [ 13.10500554,  13.10500554]]],
+            [[[ 19.5591166 ,  19.5591166 ],
+              [ 22.79202844,  22.79202844]],
+             [[ 15.54012004,  15.54012004],
+              [ 18.10873492,  18.10873492]]]]))
+    """
+    observed = np.asarray(observed)
+    if np.any(observed < 0):
+        raise ValueError("All values in `observed` must be nonnegative.")
+    if observed.size == 0:
+        raise ValueError("No data; `observed` has size 0.")
+
+    expected = expected_freq(observed)
+    if np.any(expected == 0):
+        # Include one of the positions where expected is zero in
+        # the exception message.
+        zeropos = list(np.where(expected == 0)[0])
+        raise ValueError("The internally computed table of expected "
+                         "frequencies has a zero element at %s." % zeropos)
+
+    # The degrees of freedom
+    dof = expected.size - sum(expected.shape) + expected.ndim - 1
+
+    if dof == 0:
+        # Degenerate case; this occurs when `observed` is 1D (or, more
+        # generally, when it has only one nontrivial dimension).  In this
+        # case, we also have observed == expected, so chi2 is 0.
+        chi2 = 0.0
+        p = 1.0
+    else:
+        if dof == 1 and correction:
+            # Adjust `observed` according to Yates' correction for continuity.
+            observed = observed + 0.5 * np.sign(expected - observed)
+
+        chi2, p = power_divergence(observed, expected,
+                                   ddof=observed.size - 1 - dof, axis=None,
+                                   lambda_=lambda_)
+
+    return chi2, p, dof, expected

pywafo/src/wafo/stats/kde.py

@@ -0,0 +1,513 @@
+#-------------------------------------------------------------------------------
+#
+#  Define classes for (uni/multi)-variate kernel density estimation.
+#
+#  Currently, only Gaussian kernels are implemented.
+#
+#  Written by: Robert Kern
+#
+#  Date: 2004-08-09
+#
+#  Modified: 2005-02-10 by Robert Kern.
+#              Contributed to Scipy
+#            2005-10-07 by Robert Kern.
+#              Some fixes to match the new scipy_core
+#
+#  Copyright 2004-2005 by Enthought, Inc.
+#
+#-------------------------------------------------------------------------------
+
+from __future__ import division, print_function, absolute_import
+
+# Standard library imports.
+import warnings
+
+# Scipy imports.
+from scipy.lib.six import callable, string_types
+from scipy import linalg, special
+
+from numpy import atleast_2d, reshape, zeros, newaxis, dot, exp, pi, sqrt, \
+     ravel, power, atleast_1d, squeeze, sum, transpose
+import numpy as np
+from numpy.random import randint, multivariate_normal
+
+# Local imports.
+from . import mvn
+
+
+__all__ = ['gaussian_kde']
+
+
+class gaussian_kde(object):
+    """Representation of a kernel-density estimate using Gaussian kernels.
+
+    Kernel density estimation is a way to estimate the probability density
+    function (PDF) of a random variable in a non-parametric way.
+    `gaussian_kde` works for both uni-variate and multi-variate data.   It
+    includes automatic bandwidth determination.  The estimation works best for
+    a unimodal distribution; bimodal or multi-modal distributions tend to be
+    oversmoothed.
+
+    Parameters
+    ----------
+    dataset : array_like
+        Datapoints to estimate from. In case of univariate data this is a 1-D
+        array, otherwise a 2-D array with shape (# of dims, # of data).
+    bw_method : str, scalar or callable, optional
+        The method used to calculate the estimator bandwidth.  This can be
+        'scott', 'silverman', a scalar constant or a callable.  If a scalar,
+        this will be used directly as `kde.factor`.  If a callable, it should
+        take a `gaussian_kde` instance as only parameter and return a scalar.
+        If None (default), 'scott' is used.  See Notes for more details.
+
+    Attributes
+    ----------
+    dataset : ndarray
+        The dataset with which `gaussian_kde` was initialized.
+    d : int
+        Number of dimensions.
+    n : int
+        Number of datapoints.
+    factor : float
+        The bandwidth factor, obtained from `kde.covariance_factor`, with which
+        the covariance matrix is multiplied.
+    covariance : ndarray
+        The covariance matrix of `dataset`, scaled by the calculated bandwidth
+        (`kde.factor`).
+    inv_cov : ndarray
+        The inverse of `covariance`.
+
+    Methods
+    -------
+    kde.evaluate(points) : ndarray
+        Evaluate the estimated pdf on a provided set of points.
+    kde(points) : ndarray
+        Same as kde.evaluate(points)
+    kde.integrate_gaussian(mean, cov) : float
+        Multiply pdf with a specified Gaussian and integrate over the whole
+        domain.
+    kde.integrate_box_1d(low, high) : float
+        Integrate pdf (1D only) between two bounds.
+    kde.integrate_box(low_bounds, high_bounds) : float
+        Integrate pdf over a rectangular space between low_bounds and
+        high_bounds.
+    kde.integrate_kde(other_kde) : float
+        Integrate two kernel density estimates multiplied together.
+    kde.resample(size=None) : ndarray
+        Randomly sample a dataset from the estimated pdf.
+    kde.set_bandwidth(bw_method='scott') : None
+        Computes the bandwidth, i.e. the coefficient that multiplies the data
+        covariance matrix to obtain the kernel covariance matrix.
+        .. versionadded:: 0.11.0
+    kde.covariance_factor : float
+        Computes the coefficient (`kde.factor`) that multiplies the data
+        covariance matrix to obtain the kernel covariance matrix.
+        The default is `scotts_factor`.  A subclass can overwrite this method
+        to provide a different method, or set it through a call to
+        `kde.set_bandwidth`.
+
+
+    Notes
+    -----
+    Bandwidth selection strongly influences the estimate obtained from the KDE
+    (much more so than the actual shape of the kernel).  Bandwidth selection
+    can be done by a "rule of thumb", by cross-validation, by "plug-in
+    methods" or by other means; see [3]_, [4]_ for reviews.  `gaussian_kde`
+    uses a rule of thumb, the default is Scott's Rule.
+
+    Scott's Rule [1]_, implemented as `scotts_factor`, is::
+
+        n**(-1./(d+4)),
+
+    with ``n`` the number of data points and ``d`` the number of dimensions.
+    Silverman's Rule [2]_, implemented as `silverman_factor`, is::
+
+        n * (d + 2) / 4.)**(-1. / (d + 4)).
+
+    Good general descriptions of kernel density estimation can be found in [1]_
+    and [2]_, the mathematics for this multi-dimensional implementation can be
+    found in [1]_.
+
+    References
+    ----------
+    .. [1] D.W. Scott, "Multivariate Density Estimation: Theory, Practice, and
+           Visualization", John Wiley & Sons, New York, Chicester, 1992.
+    .. [2] B.W. Silverman, "Density Estimation for Statistics and Data
+           Analysis", Vol. 26, Monographs on Statistics and Applied Probability,
+           Chapman and Hall, London, 1986.
+    .. [3] B.A. Turlach, "Bandwidth Selection in Kernel Density Estimation: A
+           Review", CORE and Institut de Statistique, Vol. 19, pp. 1-33, 1993.
+    .. [4] D.M. Bashtannyk and R.J. Hyndman, "Bandwidth selection for kernel
+           conditional density estimation", Computational Statistics & Data
+           Analysis, Vol. 36, pp. 279-298, 2001.
+
+    Examples
+    --------
+    Generate some random two-dimensional data:
+
+    >>> from scipy import stats
+    >>> def measure(n):
+    >>>     "Measurement model, return two coupled measurements."
+    >>>     m1 = np.random.normal(size=n)
+    >>>     m2 = np.random.normal(scale=0.5, size=n)
+    >>>     return m1+m2, m1-m2
+
+    >>> m1, m2 = measure(2000)
+    >>> xmin = m1.min()
+    >>> xmax = m1.max()
+    >>> ymin = m2.min()
+    >>> ymax = m2.max()
+
+    Perform a kernel density estimate on the data:
+
+    >>> X, Y = np.mgrid[xmin:xmax:100j, ymin:ymax:100j]
+    >>> positions = np.vstack([X.ravel(), Y.ravel()])
+    >>> values = np.vstack([m1, m2])
+    >>> kernel = stats.gaussian_kde(values)
+    >>> Z = np.reshape(kernel(positions).T, X.shape)
+
+    Plot the results:
+
+    >>> import matplotlib.pyplot as plt
+    >>> fig = plt.figure()
+    >>> ax = fig.add_subplot(111)
+    >>> ax.imshow(np.rot90(Z), cmap=plt.cm.gist_earth_r,
+    ...           extent=[xmin, xmax, ymin, ymax])
+    >>> ax.plot(m1, m2, 'k.', markersize=2)
+    >>> ax.set_xlim([xmin, xmax])
+    >>> ax.set_ylim([ymin, ymax])
+    >>> plt.show()
+
+    """
+    def __init__(self, dataset, bw_method=None):
+        self.dataset = atleast_2d(dataset)
+        if not self.dataset.size > 1:
+            raise ValueError("`dataset` input should have multiple elements.")
+
+        self.d, self.n = self.dataset.shape
+        self.set_bandwidth(bw_method=bw_method)
+
+    def evaluate(self, points):
+        """Evaluate the estimated pdf on a set of points.
+
+        Parameters
+        ----------
+        points : (# of dimensions, # of points)-array
+            Alternatively, a (# of dimensions,) vector can be passed in and
+            treated as a single point.
+
+        Returns
+        -------
+        values : (# of points,)-array
+            The values at each point.
+
+        Raises
+        ------
+        ValueError : if the dimensionality of the input points is different than
+                     the dimensionality of the KDE.
+
+        """
+        points = atleast_2d(points)
+
+        d, m = points.shape
+        if d != self.d:
+            if d == 1 and m == self.d:
+                # points was passed in as a row vector
+                points = reshape(points, (self.d, 1))
+                m = 1
+            else:
+                msg = "points have dimension %s, dataset has dimension %s" % (d,
+                    self.d)
+                raise ValueError(msg)
+
+        result = zeros((m,), dtype=np.float)
+
+        if m >= self.n:
+            # there are more points than data, so loop over data
+            for i in range(self.n):
+                diff = self.dataset[:, i, newaxis] - points
+                tdiff = dot(self.inv_cov, diff)
+                energy = sum(diff*tdiff,axis=0) / 2.0
+                result = result + exp(-energy)
+        else:
+            # loop over points
+            for i in range(m):
+                diff = self.dataset - points[:, i, newaxis]
+                tdiff = dot(self.inv_cov, diff)
+                energy = sum(diff * tdiff, axis=0) / 2.0
+                result[i] = sum(exp(-energy), axis=0)
+
+        result = result / self._norm_factor
+
+        return result
+
+    __call__ = evaluate
+
+    def integrate_gaussian(self, mean, cov):
+        """
+        Multiply estimated density by a multivariate Gaussian and integrate
+        over the whole space.
+
+        Parameters
+        ----------
+        mean : aray_like
+            A 1-D array, specifying the mean of the Gaussian.
+        cov : array_like
+            A 2-D array, specifying the covariance matrix of the Gaussian.
+
+        Returns
+        -------
+        result : scalar
+            The value of the integral.
+
+        Raises
+        ------
+        ValueError :
+            If the mean or covariance of the input Gaussian differs from
+            the KDE's dimensionality.
+
+        """
+        mean = atleast_1d(squeeze(mean))
+        cov = atleast_2d(cov)
+
+        if mean.shape != (self.d,):
+            raise ValueError("mean does not have dimension %s" % self.d)
+        if cov.shape != (self.d, self.d):
+            raise ValueError("covariance does not have dimension %s" % self.d)
+
+        # make mean a column vector
+        mean = mean[:, newaxis]
+
+        sum_cov = self.covariance + cov
+
+        diff = self.dataset - mean
+        tdiff = dot(linalg.inv(sum_cov), diff)
+
+        energies = sum(diff * tdiff, axis=0) / 2.0
+        result = sum(exp(-energies), axis=0) / sqrt(linalg.det(2 * pi *
+                                                        sum_cov)) / self.n
+
+        return result
+
+    def integrate_box_1d(self, low, high):
+        """
+        Computes the integral of a 1D pdf between two bounds.
+
+        Parameters
+        ----------
+        low : scalar
+            Lower bound of integration.
+        high : scalar
+            Upper bound of integration.
+
+        Returns
+        -------
+        value : scalar
+            The result of the integral.
+
+        Raises
+        ------
+        ValueError
+            If the KDE is over more than one dimension.
+
+        """
+        if self.d != 1:
+            raise ValueError("integrate_box_1d() only handles 1D pdfs")
+
+        stdev = ravel(sqrt(self.covariance))[0]
+
+        normalized_low = ravel((low - self.dataset) / stdev)
+        normalized_high = ravel((high - self.dataset) / stdev)
+
+        value = np.mean(special.ndtr(normalized_high) -
+                        special.ndtr(normalized_low))
+        return value
+
+    def integrate_box(self, low_bounds, high_bounds, maxpts=None):
+        """Computes the integral of a pdf over a rectangular interval.
+
+        Parameters
+        ----------
+        low_bounds : array_like
+            A 1-D array containing the lower bounds of integration.
+        high_bounds : array_like
+            A 1-D array containing the upper bounds of integration.
+        maxpts : int, optional
+            The maximum number of points to use for integration.
+
+        Returns
+        -------
+        value : scalar
+            The result of the integral.
+
+        """
+        if maxpts is not None:
+            extra_kwds = {'maxpts': maxpts}
+        else:
+            extra_kwds = {}
+
+        value, inform = mvn.mvnun(low_bounds, high_bounds, self.dataset,
+                                  self.covariance, **extra_kwds)
+        if inform:
+            msg = ('An integral in mvn.mvnun requires more points than %s' %
+                   (self.d * 1000))
+            warnings.warn(msg)
+
+        return value
+
+    def integrate_kde(self, other):
+        """
+        Computes the integral of the product of this  kernel density estimate
+        with another.
+
+        Parameters
+        ----------
+        other : gaussian_kde instance
+            The other kde.
+
+        Returns
+        -------
+        value : scalar
+            The result of the integral.
+
+        Raises
+        ------
+        ValueError
+            If the KDEs have different dimensionality.
+
+        """
+        if other.d != self.d:
+            raise ValueError("KDEs are not the same dimensionality")
+
+        # we want to iterate over the smallest number of points
+        if other.n < self.n:
+            small = other
+            large = self
+        else:
+            small = self
+            large = other
+
+        sum_cov = small.covariance + large.covariance
+        result = 0.0
+        for i in range(small.n):
+            mean = small.dataset[:, i, newaxis]
+            diff = large.dataset - mean
+            tdiff = dot(linalg.inv(sum_cov), diff)
+
+            energies = sum(diff * tdiff, axis=0) / 2.0
+            result += sum(exp(-energies), axis=0)
+
+        result /= sqrt(linalg.det(2 * pi * sum_cov)) * large.n * small.n
+
+        return result
+
+    def resample(self, size=None):
+        """
+        Randomly sample a dataset from the estimated pdf.
+
+        Parameters
+        ----------
+        size : int, optional
+            The number of samples to draw.  If not provided, then the size is
+            the same as the underlying dataset.
+
+        Returns
+        -------
+        resample : (self.d, `size`) ndarray
+            The sampled dataset.
+
+        """
+        if size is None:
+            size = self.n
+
+        norm = transpose(multivariate_normal(zeros((self.d,), float),
+                         self.covariance, size=size))
+        indices = randint(0, self.n, size=size)
+        means = self.dataset[:, indices]
+
+        return means + norm
+
+    def scotts_factor(self):
+        return power(self.n, -1./(self.d+4))
+
+    def silverman_factor(self):
+        return power(self.n*(self.d+2.0)/4.0, -1./(self.d+4))
+
+    #  Default method to calculate bandwidth, can be overwritten by subclass
+    covariance_factor = scotts_factor
+
+    def set_bandwidth(self, bw_method=None):
+        """Compute the estimator bandwidth with given method.
+
+        The new bandwidth calculated after a call to `set_bandwidth` is used
+        for subsequent evaluations of the estimated density.
+
+        Parameters
+        ----------
+        bw_method : str, scalar or callable, optional
+            The method used to calculate the estimator bandwidth.  This can be
+            'scott', 'silverman', a scalar constant or a callable.  If a
+            scalar, this will be used directly as `kde.factor`.  If a callable,
+            it should take a `gaussian_kde` instance as only parameter and
+            return a scalar.  If None (default), nothing happens; the current
+            `kde.covariance_factor` method is kept.
+
+        Notes
+        -----
+        .. versionadded:: 0.11
+
+        Examples
+        --------
+        >>> x1 = np.array([-7, -5, 1, 4, 5.])
+        >>> kde = stats.gaussian_kde(x1)
+        >>> xs = np.linspace(-10, 10, num=50)
+        >>> y1 = kde(xs)
+        >>> kde.set_bandwidth(bw_method='silverman')
+        >>> y2 = kde(xs)
+        >>> kde.set_bandwidth(bw_method=kde.factor / 3.)
+        >>> y3 = kde(xs)
+
+        >>> fig = plt.figure()
+        >>> ax = fig.add_subplot(111)
+        >>> ax.plot(x1, np.ones(x1.shape) / (4. * x1.size), 'bo',
+        ...         label='Data points (rescaled)')
+        >>> ax.plot(xs, y1, label='Scott (default)')
+        >>> ax.plot(xs, y2, label='Silverman')
+        >>> ax.plot(xs, y3, label='Const (1/3 * Silverman)')
+        >>> ax.legend()
+        >>> plt.show()
+
+        """
+        if bw_method is None:
+            pass
+        elif bw_method == 'scott':
+            self.covariance_factor = self.scotts_factor
+        elif bw_method == 'silverman':
+            self.covariance_factor = self.silverman_factor
+        elif np.isscalar(bw_method) and not isinstance(bw_method, string_types):
+            self._bw_method = 'use constant'
+            self.covariance_factor = lambda: bw_method
+        elif callable(bw_method):
+            self._bw_method = bw_method
+            self.covariance_factor = lambda: self._bw_method(self)
+        else:
+            msg = "`bw_method` should be 'scott', 'silverman', a scalar " \
+                  "or a callable."
+            raise ValueError(msg)
+
+        self._compute_covariance()
+
+    def _compute_covariance(self):
+        """Computes the covariance matrix for each Gaussian kernel using
+        covariance_factor().
+        """
+        self.factor = self.covariance_factor()
+        # Cache covariance and inverse covariance of the data
+        if not hasattr(self, '_data_inv_cov'):
+            self._data_covariance = atleast_2d(np.cov(self.dataset, rowvar=1,
+                                               bias=False))
+            self._data_inv_cov = linalg.inv(self._data_covariance)
+
+        self.covariance = self._data_covariance * self.factor**2
+        self.inv_cov = self._data_inv_cov / self.factor**2
+        self._norm_factor = sqrt(linalg.det(2*pi*self.covariance)) * self.n

pywafo/src/wafo/stats/mstats.py

@@ -0,0 +1,82 @@
+"""
+===================================================================
+Statistical functions for masked arrays (:mod:`scipy.stats.mstats`)
+===================================================================
+
+.. currentmodule:: scipy.stats.mstats
+
+This module contains a large number of statistical functions that can
+be used with masked arrays.
+
+Most of these functions are similar to those in scipy.stats but might
+have small differences in the API or in the algorithm used. Since this
+is a relatively new package, some API changes are still possible.
+
+.. autosummary::
+   :toctree: generated/
+
+   argstoarray
+   betai
+   chisquare
+   count_tied_groups
+   describe
+   f_oneway
+   f_value_wilks_lambda
+   find_repeats
+   friedmanchisquare
+   gmean
+   hmean
+   kendalltau
+   kendalltau_seasonal
+   kruskalwallis
+   kruskalwallis
+   ks_twosamp
+   ks_twosamp
+   kurtosis
+   kurtosistest
+   linregress
+   mannwhitneyu
+   plotting_positions
+   mode
+   moment
+   mquantiles
+   msign
+   normaltest
+   obrientransform
+   pearsonr
+   plotting_positions
+   pointbiserialr
+   rankdata
+   scoreatpercentile
+   sem
+   signaltonoise
+   skew
+   skewtest
+   spearmanr
+   theilslopes
+   threshold
+   tmax
+   tmean
+   tmin
+   trim
+   trima
+   trimboth
+   trimmed_stde
+   trimr
+   trimtail
+   tsem
+   ttest_onesamp
+   ttest_ind
+   ttest_onesamp
+   ttest_rel
+   tvar
+   variation
+   winsorize
+   zmap
+   zscore
+
+"""
+from __future__ import division, print_function, absolute_import
+
+from .mstats_basic import *
+from .mstats_extras import *

pywafo/src/wafo/stats/mstats_extras.py

@@ -0,0 +1,466 @@
+"""
+Additional statistics functions, with support to MA.
+
+:author: Pierre GF Gerard-Marchant
+:contact: pierregm_at_uga_edu
+:date: $Date: 2007-10-29 17:18:13 +0200 (Mon, 29 Oct 2007) $
+:version: $Id: morestats.py 3473 2007-10-29 15:18:13Z jarrod.millman $
+"""
+from __future__ import division, print_function, absolute_import
+
+__author__ = "Pierre GF Gerard-Marchant"
+__docformat__ = "restructuredtext en"
+
+
+__all__ = ['compare_medians_ms',
+           'hdquantiles', 'hdmedian', 'hdquantiles_sd',
+           'idealfourths',
+           'median_cihs','mjci','mquantiles_cimj',
+           'rsh',
+           'trimmed_mean_ci',]
+
+import numpy as np
+from numpy import float_, int_, ndarray
+
+import numpy.ma as ma
+from numpy.ma import MaskedArray
+
+from . import mstats_basic as mstats
+
+from scipy.stats.distributions import norm, beta, t, binom
+
+
+#####--------------------------------------------------------------------------
+#---- --- Quantiles ---
+#####--------------------------------------------------------------------------
+def hdquantiles(data, prob=list([.25,.5,.75]), axis=None, var=False,):
+    """
+    Computes quantile estimates with the Harrell-Davis method.
+
+    The quantile estimates are calculated as a weighted linear combination
+    of order statistics.
+
+    Parameters
+    ----------
+    data : array_like
+        Data array.
+    prob : sequence
+        Sequence of quantiles to compute.
+    axis : int
+        Axis along which to compute the quantiles. If None, use a flattened
+        array.
+    var : boolean
+        Whether to return the variance of the estimate.
+
+    Returns
+    -------
+    hdquantiles : MaskedArray
+        A (p,) array of quantiles (if `var` is False), or a (2,p) array of
+        quantiles and variances (if `var` is True), where ``p`` is the
+        number of quantiles.
+
+    """
+    def _hd_1D(data,prob,var):
+        "Computes the HD quantiles for a 1D array. Returns nan for invalid data."
+        xsorted = np.squeeze(np.sort(data.compressed().view(ndarray)))
+        # Don't use length here, in case we have a numpy scalar
+        n = xsorted.size
+        #.........
+        hd = np.empty((2,len(prob)), float_)
+        if n < 2:
+            hd.flat = np.nan
+            if var:
+                return hd
+            return hd[0]
+        #.........
+        v = np.arange(n+1) / float(n)
+        betacdf = beta.cdf
+        for (i,p) in enumerate(prob):
+            _w = betacdf(v, (n+1)*p, (n+1)*(1-p))
+            w = _w[1:] - _w[:-1]
+            hd_mean = np.dot(w, xsorted)
+            hd[0,i] = hd_mean
+            #
+            hd[1,i] = np.dot(w, (xsorted-hd_mean)**2)
+            #
+        hd[0, prob == 0] = xsorted[0]
+        hd[0, prob == 1] = xsorted[-1]
+        if var:
+            hd[1, prob == 0] = hd[1, prob == 1] = np.nan
+            return hd
+        return hd[0]
+    # Initialization & checks ---------
+    data = ma.array(data, copy=False, dtype=float_)
+    p = np.array(prob, copy=False, ndmin=1)
+    # Computes quantiles along axis (or globally)
+    if (axis is None) or (data.ndim == 1):
+        result = _hd_1D(data, p, var)
+    else:
+        if data.ndim > 2:
+            raise ValueError("Array 'data' must be at most two dimensional, but got data.ndim = %d" % data.ndim)
+        result = ma.apply_along_axis(_hd_1D, axis, data, p, var)
+    #
+    return ma.fix_invalid(result, copy=False)
+
+#..............................................................................
+
+
+def hdmedian(data, axis=-1, var=False):
+    """
+    Returns the Harrell-Davis estimate of the median along the given axis.
+
+    Parameters
+    ----------
+    data : ndarray
+        Data array.
+    axis : int
+        Axis along which to compute the quantiles. If None, use a flattened
+        array.
+    var : boolean
+        Whether to return the variance of the estimate.
+
+    """
+    result = hdquantiles(data,[0.5], axis=axis, var=var)
+    return result.squeeze()
+
+
+#..............................................................................
+def hdquantiles_sd(data, prob=list([.25,.5,.75]), axis=None):
+    """
+    The standard error of the Harrell-Davis quantile estimates by jackknife.
+
+    Parameters
+    ----------
+    data : array_like
+        Data array.
+    prob : sequence
+        Sequence of quantiles to compute.
+    axis : int
+        Axis along which to compute the quantiles. If None, use a flattened
+        array.
+
+    Returns
+    -------
+    hdquantiles_sd : MaskedArray
+        Standard error of the Harrell-Davis quantile estimates.
+
+    """
+    def _hdsd_1D(data,prob):
+        "Computes the std error for 1D arrays."
+        xsorted = np.sort(data.compressed())
+        n = len(xsorted)
+        #.........
+        hdsd = np.empty(len(prob), float_)
+        if n < 2:
+            hdsd.flat = np.nan
+        #.........
+        vv = np.arange(n) / float(n-1)
+        betacdf = beta.cdf
+        #
+        for (i,p) in enumerate(prob):
+            _w = betacdf(vv, (n+1)*p, (n+1)*(1-p))
+            w = _w[1:] - _w[:-1]
+            mx_ = np.fromiter([np.dot(w,xsorted[np.r_[list(range(0,k)),
+                                                      list(range(k+1,n))].astype(int_)])
+                                  for k in range(n)], dtype=float_)
+            mx_var = np.array(mx_.var(), copy=False, ndmin=1) * n / float(n-1)
+            hdsd[i] = float(n-1) * np.sqrt(np.diag(mx_var).diagonal() / float(n))
+        return hdsd
+    # Initialization & checks ---------
+    data = ma.array(data, copy=False, dtype=float_)
+    p = np.array(prob, copy=False, ndmin=1)
+    # Computes quantiles along axis (or globally)
+    if (axis is None):
+        result = _hdsd_1D(data, p)
+    else:
+        if data.ndim > 2:
+            raise ValueError("Array 'data' must be at most two dimensional, but got data.ndim = %d" % data.ndim)
+        result = ma.apply_along_axis(_hdsd_1D, axis, data, p)
+    #
+    return ma.fix_invalid(result, copy=False).ravel()
+
+
+#####--------------------------------------------------------------------------
+#---- --- Confidence intervals ---
+#####--------------------------------------------------------------------------
+
+def trimmed_mean_ci(data, limits=(0.2,0.2), inclusive=(True,True),
+                    alpha=0.05, axis=None):
+    """
+    Selected confidence interval of the trimmed mean along the given axis.
+
+    Parameters
+    ----------
+    data : array_like
+        Input data.
+    limits : {None, tuple}, optional
+        None or a two item tuple.
+        Tuple of the percentages to cut on each side of the array, with respect
+        to the number of unmasked data, as floats between 0. and 1. If ``n``
+        is the number of unmasked data before trimming, then
+        (``n`` * `limits[0]`)th smallest data and (``n`` * `limits[1]`)th
+        largest data are masked.  The total number of unmasked data after
+        trimming is ``n`` * (1. - sum(`limits`)).
+        The value of one limit can be set to None to indicate an open interval.
+
+        Defaults to (0.2, 0.2).
+    inclusive : (2,) tuple of boolean, optional
+        If relative==False, tuple indicating whether values exactly equal to
+        the absolute limits are allowed.
+        If relative==True, tuple indicating whether the number of data being
+        masked on each side should be rounded (True) or truncated (False).
+
+        Defaults to (True, True).
+    alpha : float, optional
+        Confidence level of the intervals.
+
+        Defaults to 0.05.
+    axis : int, optional
+        Axis along which to cut. If None, uses a flattened version of `data`.
+
+        Defaults to None.
+
+    Returns
+    -------
+    trimmed_mean_ci : (2,) ndarray
+        The lower and upper confidence intervals of the trimmed data.
+
+    """
+    data = ma.array(data, copy=False)
+    trimmed = mstats.trimr(data, limits=limits, inclusive=inclusive, axis=axis)
+    tmean = trimmed.mean(axis)
+    tstde = mstats.trimmed_stde(data,limits=limits,inclusive=inclusive,axis=axis)
+    df = trimmed.count(axis) - 1
+    tppf = t.ppf(1-alpha/2.,df)
+    return np.array((tmean - tppf*tstde, tmean+tppf*tstde))
+
+#..............................................................................
+
+
+def mjci(data, prob=[0.25,0.5,0.75], axis=None):
+    """
+    Returns the Maritz-Jarrett estimators of the standard error of selected
+    experimental quantiles of the data.
+
+    Parameters
+    ----------
+    data: ndarray
+        Data array.
+    prob: sequence
+        Sequence of quantiles to compute.
+    axis : int
+        Axis along which to compute the quantiles. If None, use a flattened
+        array.
+
+    """
+    def _mjci_1D(data, p):
+        data = np.sort(data.compressed())
+        n = data.size
+        prob = (np.array(p) * n + 0.5).astype(int_)
+        betacdf = beta.cdf
+        #
+        mj = np.empty(len(prob), float_)
+        x = np.arange(1,n+1, dtype=float_) / n
+        y = x - 1./n
+        for (i,m) in enumerate(prob):
+            (m1,m2) = (m-1, n-m)
+            W = betacdf(x,m-1,n-m) - betacdf(y,m-1,n-m)
+            C1 = np.dot(W,data)
+            C2 = np.dot(W,data**2)
+            mj[i] = np.sqrt(C2 - C1**2)
+        return mj
+    #
+    data = ma.array(data, copy=False)
+    if data.ndim > 2:
+        raise ValueError("Array 'data' must be at most two dimensional, but got data.ndim = %d" % data.ndim)
+    p = np.array(prob, copy=False, ndmin=1)
+    # Computes quantiles along axis (or globally)
+    if (axis is None):
+        return _mjci_1D(data, p)
+    else:
+        return ma.apply_along_axis(_mjci_1D, axis, data, p)
+
+#..............................................................................
+
+
+def mquantiles_cimj(data, prob=[0.25,0.50,0.75], alpha=0.05, axis=None):
+    """
+    Computes the alpha confidence interval for the selected quantiles of the
+    data, with Maritz-Jarrett estimators.
+
+    Parameters
+    ----------
+    data : ndarray
+        Data array.
+    prob : sequence
+        Sequence of quantiles to compute.
+    alpha : float
+        Confidence level of the intervals.
+    axis : integer
+        Axis along which to compute the quantiles.
+        If None, use a flattened array.
+
+    """
+    alpha = min(alpha, 1-alpha)
+    z = norm.ppf(1-alpha/2.)
+    xq = mstats.mquantiles(data, prob, alphap=0, betap=0, axis=axis)
+    smj = mjci(data, prob, axis=axis)
+    return (xq - z * smj, xq + z * smj)
+
+
+#.............................................................................
+def median_cihs(data, alpha=0.05, axis=None):
+    """
+    Computes the alpha-level confidence interval for the median of the data.
+
+    Uses the Hettmasperger-Sheather method.
+
+    Parameters
+    ----------
+    data : array_like
+        Input data. Masked values are discarded. The input should be 1D only,
+        or `axis` should be set to None.
+    alpha : float
+        Confidence level of the intervals.
+    axis : integer
+        Axis along which to compute the quantiles. If None, use a flattened
+        array.
+
+    Returns
+    -------
+    median_cihs :
+        Alpha level confidence interval.
+
+    """
+    def _cihs_1D(data, alpha):
+        data = np.sort(data.compressed())
+        n = len(data)
+        alpha = min(alpha, 1-alpha)
+        k = int(binom._ppf(alpha/2., n, 0.5))
+        gk = binom.cdf(n-k,n,0.5) - binom.cdf(k-1,n,0.5)
+        if gk < 1-alpha:
+            k -= 1
+            gk = binom.cdf(n-k,n,0.5) - binom.cdf(k-1,n,0.5)
+        gkk = binom.cdf(n-k-1,n,0.5) - binom.cdf(k,n,0.5)
+        I = (gk - 1 + alpha)/(gk - gkk)
+        lambd = (n-k) * I / float(k + (n-2*k)*I)
+        lims = (lambd*data[k] + (1-lambd)*data[k-1],
+                lambd*data[n-k-1] + (1-lambd)*data[n-k])
+        return lims
+    data = ma.rray(data, copy=False)
+    # Computes quantiles along axis (or globally)
+    if (axis is None):
+        result = _cihs_1D(data.compressed(), alpha)
+    else:
+        if data.ndim > 2:
+            raise ValueError("Array 'data' must be at most two dimensional, but got data.ndim = %d" % data.ndim)
+        result = ma.apply_along_axis(_cihs_1D, axis, data, alpha)
+    #
+    return result
+
+#..............................................................................
+
+
+def compare_medians_ms(group_1, group_2, axis=None):
+    """
+    Compares the medians from two independent groups along the given axis.
+
+    The comparison is performed using the McKean-Schrader estimate of the
+    standard error of the medians.
+
+    Parameters
+    ----------
+    group_1 : array_like
+        First dataset.
+    group_2 : array_like
+        Second dataset.
+    axis : int, optional
+        Axis along which the medians are estimated. If None, the arrays are
+        flattened.  If `axis` is not None, then `group_1` and `group_2`
+        should have the same shape.
+
+    Returns
+    -------
+    compare_medians_ms : {float, ndarray}
+        If `axis` is None, then returns a float, otherwise returns a 1-D
+        ndarray of floats with a length equal to the length of `group_1`
+        along `axis`.
+
+    """
+    (med_1, med_2) = (ma.median(group_1,axis=axis), ma.median(group_2,axis=axis))
+    (std_1, std_2) = (mstats.stde_median(group_1, axis=axis),
+                      mstats.stde_median(group_2, axis=axis))
+    W = np.abs(med_1 - med_2) / ma.sqrt(std_1**2 + std_2**2)
+    return 1 - norm.cdf(W)
+
+
+def idealfourths(data, axis=None):
+    """
+    Returns an estimate of the lower and upper quartiles.
+
+    Uses the ideal fourths algorithm.
+
+    Parameters
+    ----------
+    data : array_like
+        Input array.
+    axis : int, optional
+        Axis along which the quartiles are estimated. If None, the arrays are
+        flattened.
+
+    Returns
+    -------
+    idealfourths : {list of floats, masked array}
+        Returns the two internal values that divide `data` into four parts
+        using the ideal fourths algorithm either along the flattened array
+        (if `axis` is None) or along `axis` of `data`.
+
+    """
+    def _idf(data):
+        x = data.compressed()
+        n = len(x)
+        if n < 3:
+            return [np.nan,np.nan]
+        (j,h) = divmod(n/4. + 5/12.,1)
+        j = int(j)
+        qlo = (1-h)*x[j-1] + h*x[j]
+        k = n - j
+        qup = (1-h)*x[k] + h*x[k-1]
+        return [qlo, qup]
+    data = ma.sort(data, axis=axis).view(MaskedArray)
+    if (axis is None):
+        return _idf(data)
+    else:
+        return ma.apply_along_axis(_idf, axis, data)
+
+
+def rsh(data, points=None):
+    """
+    Evaluates Rosenblatt's shifted histogram estimators for each point
+    on the dataset 'data'.
+
+    Parameters
+    ----------
+    data : sequence
+        Input data. Masked values are ignored.
+    points : sequence
+        Sequence of points where to evaluate Rosenblatt shifted histogram.
+        If None, use the data.
+
+    """
+    data = ma.array(data, copy=False)
+    if points is None:
+        points = data
+    else:
+        points = np.array(points, copy=False, ndmin=1)
+    if data.ndim != 1:
+        raise AttributeError("The input array should be 1D only !")
+    n = data.count()
+    r = idealfourths(data, axis=None)
+    h = 1.2 * (r[-1]-r[0]) / n**(1./5)
+    nhi = (data[:,None] <= points[None,:] + h).sum(0)
+    nlo = (data[:,None] < points[None,:] - h).sum(0)
+    return (nhi-nlo) / (2.*n*h)
+
+
+###############################################################################

pywafo/src/wafo/stats/rv.py

@@ -0,0 +1,76 @@
+from __future__ import division, print_function, absolute_import
+
+from numpy import vectorize, deprecate
+from numpy.random import random_sample
+
+__all__ = ['randwppf', 'randwcdf']
+
+# XXX: Are these needed anymore?
+
+#####################################
+# General purpose continuous
+######################################
+
+
+@deprecate(message="Deprecated in scipy 0.14.0, use "
+                   "distribution-specific rvs() method instead")
+def randwppf(ppf, args=(), size=None):
+    """
+    returns an array of randomly distributed integers of a distribution
+    whose percent point function (inverse of the CDF or quantile function)
+    is given.
+
+    args is a tuple of extra arguments to the ppf function (i.e. shape,
+    location, scale), and size is the size of the output.  Note the ppf
+    function must accept an array of q values to compute over.
+
+    """
+    U = random_sample(size=size)
+    return ppf(*(U,)+args)
+
+
+@deprecate(message="Deprecated in scipy 0.14.0, use "
+                   "distribution-specific rvs() method instead")
+def randwcdf(cdf, mean=1.0, args=(), size=None):
+    """
+    Returns an array of randomly distributed integers given a CDF.
+
+    Given a cumulative distribution function (CDF) returns an array of
+    randomly distributed integers that would satisfy the CDF.
+
+    Parameters
+    ----------
+    cdf : function
+        CDF function that accepts a single value and `args`, and returns
+        an single value.
+    mean : float, optional
+        The mean of the distribution which helps the solver.  Defaults
+        to 1.0.
+    args : tuple, optional
+        Extra arguments to the cdf function (i.e. shape, location, scale)
+    size : {int, None}, optional
+        Is the size of the output.  If None, only 1 value will be returned.
+
+    Returns
+    -------
+    randwcdf : ndarray
+        Array of random numbers.
+
+    Notes
+    -----
+    Can use the ``scipy.stats.distributions.*.cdf`` functions for the
+    `cdf` parameter.
+
+    """
+    import scipy.optimize as optimize
+
+    def _ppfopt(x, q, *nargs):
+        newargs = (x,)+nargs
+        return cdf(*newargs) - q
+
+    def _ppf(q, *nargs):
+        return optimize.fsolve(_ppfopt, mean, args=(q,)+nargs)
+
+    _vppf = vectorize(_ppf)
+    U = random_sample(size=size)
+    return _vppf(*(U,)+args)

pywafo/src/wafo/stats/six.py

@@ -307,7 +307,7 @@ _add_doc(u, """Text literal""")
 
 
 if PY3:
-    import builtins
+    import builtins  # @UnresolvedImport
     exec_ = getattr(builtins, "exec")
 
     def reraise(tp, value, tb=None):

pywafo/src/wafo/stats/tests/common_tests.py

@@ -0,0 +1,154 @@
+from __future__ import division, print_function, absolute_import
+
+import inspect
+import warnings
+
+import numpy as np
+import numpy.testing as npt
+
+#from scipy.lib._version import NumpyVersion
+from scipy import stats
+
+
+#NUMPY_BELOW_1_7 = NumpyVersion(np.__version__) < '1.7.0'
+NUMPY_BELOW_1_7 =np.__version__ < '1.7.0'
+
+
+def check_normalization(distfn, args, distname):
+    norm_moment = distfn.moment(0, *args)
+    npt.assert_allclose(norm_moment, 1.0)
+
+    # this is a temporary plug: either ncf or expect is problematic;
+    # best be marked as a knownfail, but I've no clue how to do it.
+    if distname == "ncf":
+        atol, rtol = 1e-5, 0
+    else:
+        atol, rtol = 1e-7, 1e-7
+
+    normalization_expect = distfn.expect(lambda x: 1, args=args)
+    npt.assert_allclose(normalization_expect, 1.0, atol=atol, rtol=rtol,
+            err_msg=distname, verbose=True)
+
+    normalization_cdf = distfn.cdf(distfn.b, *args)
+    npt.assert_allclose(normalization_cdf, 1.0)
+
+
+def check_moment(distfn, arg, m, v, msg):
+    m1 = distfn.moment(1, *arg)
+    m2 = distfn.moment(2, *arg)
+    if not np.isinf(m):
+        npt.assert_almost_equal(m1, m, decimal=10, err_msg=msg +
+                            ' - 1st moment')
+    else:                     # or np.isnan(m1),
+        npt.assert_(np.isinf(m1),
+               msg + ' - 1st moment -infinite, m1=%s' % str(m1))
+
+    if not np.isinf(v):
+        npt.assert_almost_equal(m2 - m1 * m1, v, decimal=10, err_msg=msg +
+                            ' - 2ndt moment')
+    else:                     # or np.isnan(m2),
+        npt.assert_(np.isinf(m2),
+               msg + ' - 2nd moment -infinite, m2=%s' % str(m2))
+
+
+def check_mean_expect(distfn, arg, m, msg):
+    if np.isfinite(m):
+        m1 = distfn.expect(lambda x: x, arg)
+        npt.assert_almost_equal(m1, m, decimal=5, err_msg=msg +
+                            ' - 1st moment (expect)')
+
+
+def check_var_expect(distfn, arg, m, v, msg):
+    if np.isfinite(v):
+        m2 = distfn.expect(lambda x: x*x, arg)
+        npt.assert_almost_equal(m2, v + m*m, decimal=5, err_msg=msg +
+                            ' - 2st moment (expect)')
+
+
+def check_skew_expect(distfn, arg, m, v, s, msg):
+    if np.isfinite(s):
+        m3e = distfn.expect(lambda x: np.power(x-m, 3), arg)
+        npt.assert_almost_equal(m3e, s * np.power(v, 1.5),
+                decimal=5, err_msg=msg + ' - skew')
+    else:
+        npt.assert_(np.isnan(s))
+
+
+def check_kurt_expect(distfn, arg, m, v, k, msg):
+    if np.isfinite(k):
+        m4e = distfn.expect(lambda x: np.power(x-m, 4), arg)
+        npt.assert_allclose(m4e, (k + 3.) * np.power(v, 2), atol=1e-5, rtol=1e-5,
+                err_msg=msg + ' - kurtosis')
+    else:
+        npt.assert_(np.isnan(k))
+
+
+def check_entropy(distfn, arg, msg):
+    ent = distfn.entropy(*arg)
+    npt.assert_(not np.isnan(ent), msg + 'test Entropy is nan')
+
+
+def check_private_entropy(distfn, args, superclass):
+    # compare a generic _entropy with the distribution-specific implementation
+    npt.assert_allclose(distfn._entropy(*args),
+                        superclass._entropy(distfn, *args))
+
+
+def check_edge_support(distfn, args):
+    # Make sure the x=self.a and self.b are handled correctly.
+    x = [distfn.a, distfn.b]
+    if isinstance(distfn, stats.rv_continuous):
+        npt.assert_equal(distfn.cdf(x, *args), [0.0, 1.0])
+        npt.assert_equal(distfn.logcdf(x, *args), [-np.inf, 0.0])
+
+        npt.assert_equal(distfn.sf(x, *args), [1.0, 0.0])
+        npt.assert_equal(distfn.logsf(x, *args), [0.0, -np.inf])
+
+    if isinstance(distfn, stats.rv_discrete):
+        x = [distfn.a - 1, distfn.b]
+    npt.assert_equal(distfn.ppf([0.0, 1.0], *args), x)
+    npt.assert_equal(distfn.isf([0.0, 1.0], *args), x[::-1])
+
+    # out-of-bounds for isf & ppf
+    npt.assert_(np.isnan(distfn.isf([-1, 2], *args)).all())
+    npt.assert_(np.isnan(distfn.ppf([-1, 2], *args)).all())
+
+
+def check_named_args(distfn, x, shape_args, defaults, meths):
+    ## Check calling w/ named arguments.
+
+    # check consistency of shapes, numargs and _parse signature
+    signature = inspect.getargspec(distfn._parse_args)
+    npt.assert_(signature.varargs is None)
+    npt.assert_(signature.keywords is None)
+    npt.assert_(signature.defaults == defaults)
+
+    shape_argnames = signature.args[1:-len(defaults)]  # self, a, b, loc=0, scale=1
+    if distfn.shapes:
+        shapes_ = distfn.shapes.replace(',', ' ').split()
+    else:
+        shapes_ = ''
+    npt.assert_(len(shapes_) == distfn.numargs)
+    npt.assert_(len(shapes_) == len(shape_argnames))
+
+    # check calling w/ named arguments
+    shape_args = list(shape_args)
+
+    vals = [meth(x, *shape_args) for meth in meths]
+    npt.assert_(np.all(np.isfinite(vals)))
+
+    names, a, k = shape_argnames[:], shape_args[:], {}
+    while names:
+        k.update({names.pop(): a.pop()})
+        v = [meth(x, *a, **k) for meth in meths]
+        npt.assert_array_equal(vals, v)
+        if not 'n' in k.keys():
+            # `n` is first parameter of moment(), so can't be used as named arg
+            with warnings.catch_warnings():
+                warnings.simplefilter("ignore", UserWarning)
+                npt.assert_equal(distfn.moment(1, *a, **k),
+                                 distfn.moment(1, *shape_args))
+
+    # unknown arguments should not go through:
+    k.update({'kaboom': 42})
+    npt.assert_raises(TypeError, distfn.cdf, x, **k)

pywafo/src/wafo/stats/tests/test_binned_statistic.py

@@ -0,0 +1,238 @@
+from __future__ import division, print_function, absolute_import
+
+import numpy as np
+from numpy.testing import assert_array_almost_equal, run_module_suite
+from scipy.stats import \
+    binned_statistic, binned_statistic_2d, binned_statistic_dd
+
+
+class TestBinnedStatistic(object):
+
+    @classmethod
+    def setup_class(cls):
+        np.random.seed(9865)
+        cls.x = np.random.random(100)
+        cls.y = np.random.random(100)
+        cls.v = np.random.random(100)
+        cls.X = np.random.random((100, 3))
+
+    def test_1d_count(self):
+        x = self.x
+        v = self.v
+
+        count1, edges1, bc = binned_statistic(x, v, 'count', bins=10)
+        count2, edges2 = np.histogram(x, bins=10)
+
+        assert_array_almost_equal(count1, count2)
+        assert_array_almost_equal(edges1, edges2)
+
+    def test_1d_sum(self):
+        x = self.x
+        v = self.v
+
+        sum1, edges1, bc = binned_statistic(x, v, 'sum', bins=10)
+        sum2, edges2 = np.histogram(x, bins=10, weights=v)
+
+        assert_array_almost_equal(sum1, sum2)
+        assert_array_almost_equal(edges1, edges2)
+
+    def test_1d_mean(self):
+        x = self.x
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic(x, v, 'mean', bins=10)
+        stat2, edges2, bc = binned_statistic(x, v, np.mean, bins=10)
+
+        assert_array_almost_equal(stat1, stat2)
+        assert_array_almost_equal(edges1, edges2)
+
+    def test_1d_std(self):
+        x = self.x
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic(x, v, 'std', bins=10)
+        stat2, edges2, bc = binned_statistic(x, v, np.std, bins=10)
+
+        assert_array_almost_equal(stat1, stat2)
+        assert_array_almost_equal(edges1, edges2)
+
+    def test_1d_median(self):
+        x = self.x
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic(x, v, 'median', bins=10)
+        stat2, edges2, bc = binned_statistic(x, v, np.median, bins=10)
+
+        assert_array_almost_equal(stat1, stat2)
+        assert_array_almost_equal(edges1, edges2)
+
+    def test_1d_bincode(self):
+        x = self.x[:20]
+        v = self.v[:20]
+
+        count1, edges1, bc = binned_statistic(x, v, 'count', bins=3)
+        bc2 = np.array([3, 2, 1, 3, 2, 3, 3, 3, 3, 1, 1, 3, 3, 1, 2, 3, 1,
+                        1, 2, 1])
+
+        bcount = [(bc == i).sum() for i in np.unique(bc)]
+
+        assert_array_almost_equal(bc, bc2)
+        assert_array_almost_equal(bcount, count1)
+
+    def test_1d_range_keyword(self):
+        # Regression test for gh-3063, range can be (min, max) or [(min, max)]
+        np.random.seed(9865)
+        x = np.arange(30)
+        data = np.random.random(30)
+
+        mean, bins, _ = binned_statistic(x[:15], data[:15])
+        mean_range, bins_range, _ = binned_statistic(x, data, range=[(0, 14)])
+        mean_range2, bins_range2, _ = binned_statistic(x, data, range=(0, 14))
+
+        assert_array_almost_equal(mean, mean_range)
+        assert_array_almost_equal(bins, bins_range)
+        assert_array_almost_equal(mean, mean_range2)
+        assert_array_almost_equal(bins, bins_range2)
+
+    def test_2d_count(self):
+        x = self.x
+        y = self.y
+        v = self.v
+
+        count1, binx1, biny1, bc = binned_statistic_2d(x, y, v, 'count', bins=5)
+        count2, binx2, biny2 = np.histogram2d(x, y, bins=5)
+
+        assert_array_almost_equal(count1, count2)
+        assert_array_almost_equal(binx1, binx2)
+        assert_array_almost_equal(biny1, biny2)
+
+    def test_2d_sum(self):
+        x = self.x
+        y = self.y
+        v = self.v
+
+        sum1, binx1, biny1, bc = binned_statistic_2d(x, y, v, 'sum', bins=5)
+        sum2, binx2, biny2 = np.histogram2d(x, y, bins=5, weights=v)
+
+        assert_array_almost_equal(sum1, sum2)
+        assert_array_almost_equal(binx1, binx2)
+        assert_array_almost_equal(biny1, biny2)
+
+    def test_2d_mean(self):
+        x = self.x
+        y = self.y
+        v = self.v
+
+        stat1, binx1, biny1, bc = binned_statistic_2d(x, y, v, 'mean', bins=5)
+        stat2, binx2, biny2, bc = binned_statistic_2d(x, y, v, np.mean, bins=5)
+
+        assert_array_almost_equal(stat1, stat2)
+        assert_array_almost_equal(binx1, binx2)
+        assert_array_almost_equal(biny1, biny2)
+
+    def test_2d_std(self):
+        x = self.x
+        y = self.y
+        v = self.v
+
+        stat1, binx1, biny1, bc = binned_statistic_2d(x, y, v, 'std', bins=5)
+        stat2, binx2, biny2, bc = binned_statistic_2d(x, y, v, np.std, bins=5)
+
+        assert_array_almost_equal(stat1, stat2)
+        assert_array_almost_equal(binx1, binx2)
+        assert_array_almost_equal(biny1, biny2)
+
+    def test_2d_median(self):
+        x = self.x
+        y = self.y
+        v = self.v
+
+        stat1, binx1, biny1, bc = binned_statistic_2d(x, y, v, 'median', bins=5)
+        stat2, binx2, biny2, bc = binned_statistic_2d(x, y, v, np.median, bins=5)
+
+        assert_array_almost_equal(stat1, stat2)
+        assert_array_almost_equal(binx1, binx2)
+        assert_array_almost_equal(biny1, biny2)
+
+    def test_2d_bincode(self):
+        x = self.x[:20]
+        y = self.y[:20]
+        v = self.v[:20]
+
+        count1, binx1, biny1, bc = binned_statistic_2d(x, y, v, 'count', bins=3)
+        bc2 = np.array([17, 11, 6, 16, 11, 17, 18, 17, 17, 7, 6, 18, 16,
+                        6, 11, 16, 6, 6, 11, 8])
+
+        bcount = [(bc == i).sum() for i in np.unique(bc)]
+
+        assert_array_almost_equal(bc, bc2)
+        count1adj = count1[count1.nonzero()]
+        assert_array_almost_equal(bcount, count1adj)
+
+    def test_dd_count(self):
+        X = self.X
+        v = self.v
+
+        count1, edges1, bc = binned_statistic_dd(X, v, 'count', bins=3)
+        count2, edges2 = np.histogramdd(X, bins=3)
+
+        assert_array_almost_equal(count1, count2)
+        assert_array_almost_equal(edges1, edges2)
+
+    def test_dd_sum(self):
+        X = self.X
+        v = self.v
+
+        sum1, edges1, bc = binned_statistic_dd(X, v, 'sum', bins=3)
+        sum2, edges2 = np.histogramdd(X, bins=3, weights=v)
+
+        assert_array_almost_equal(sum1, sum2)
+        assert_array_almost_equal(edges1, edges2)
+
+    def test_dd_mean(self):
+        X = self.X
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic_dd(X, v, 'mean', bins=3)
+        stat2, edges2, bc = binned_statistic_dd(X, v, np.mean, bins=3)
+
+        assert_array_almost_equal(stat1, stat2)
+        assert_array_almost_equal(edges1, edges2)
+
+    def test_dd_std(self):
+        X = self.X
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic_dd(X, v, 'std', bins=3)
+        stat2, edges2, bc = binned_statistic_dd(X, v, np.std, bins=3)
+
+        assert_array_almost_equal(stat1, stat2)
+        assert_array_almost_equal(edges1, edges2)
+
+    def test_dd_median(self):
+        X = self.X
+        v = self.v
+
+        stat1, edges1, bc = binned_statistic_dd(X, v, 'median', bins=3)
+        stat2, edges2, bc = binned_statistic_dd(X, v, np.median, bins=3)
+
+        assert_array_almost_equal(stat1, stat2)
+        assert_array_almost_equal(edges1, edges2)
+
+    def test_dd_bincode(self):
+        X = self.X[:20]
+        v = self.v[:20]
+
+        count1, edges1, bc = binned_statistic_dd(X, v, 'count', bins=3)
+        bc2 = np.array([63, 33, 86, 83, 88, 67, 57, 33, 42, 41, 82, 83, 92,
+                        32, 36, 91, 43, 87, 81, 81])
+
+        bcount = [(bc == i).sum() for i in np.unique(bc)]
+
+        assert_array_almost_equal(bc, bc2)
+        count1adj = count1[count1.nonzero()]
+        assert_array_almost_equal(bcount, count1adj)
+
+
+if __name__ == "__main__":
+    run_module_suite()

pywafo/src/wafo/stats/tests/test_contingency.py

@@ -0,0 +1,202 @@
+from __future__ import division, print_function, absolute_import
+
+import numpy as np
+from numpy.testing import (run_module_suite, assert_equal, assert_array_equal,
+         assert_array_almost_equal, assert_approx_equal, assert_raises,
+         assert_allclose)
+from scipy.special import xlogy
+from scipy.stats.contingency import margins, expected_freq, chi2_contingency
+
+
+def test_margins():
+    a = np.array([1])
+    m = margins(a)
+    assert_equal(len(m), 1)
+    m0 = m[0]
+    assert_array_equal(m0, np.array([1]))
+
+    a = np.array([[1]])
+    m0, m1 = margins(a)
+    expected0 = np.array([[1]])
+    expected1 = np.array([[1]])
+    assert_array_equal(m0, expected0)
+    assert_array_equal(m1, expected1)
+
+    a = np.arange(12).reshape(2, 6)
+    m0, m1 = margins(a)
+    expected0 = np.array([[15], [51]])
+    expected1 = np.array([[6, 8, 10, 12, 14, 16]])
+    assert_array_equal(m0, expected0)
+    assert_array_equal(m1, expected1)
+
+    a = np.arange(24).reshape(2, 3, 4)
+    m0, m1, m2 = margins(a)
+    expected0 = np.array([[[66]], [[210]]])
+    expected1 = np.array([[[60], [92], [124]]])
+    expected2 = np.array([[[60, 66, 72, 78]]])
+    assert_array_equal(m0, expected0)
+    assert_array_equal(m1, expected1)
+    assert_array_equal(m2, expected2)
+
+
+def test_expected_freq():
+    assert_array_equal(expected_freq([1]), np.array([1.0]))
+
+    observed = np.array([[[2, 0], [0, 2]], [[0, 2], [2, 0]], [[1, 1], [1, 1]]])
+    e = expected_freq(observed)
+    assert_array_equal(e, np.ones_like(observed))
+
+    observed = np.array([[10, 10, 20], [20, 20, 20]])
+    e = expected_freq(observed)
+    correct = np.array([[12., 12., 16.], [18., 18., 24.]])
+    assert_array_almost_equal(e, correct)
+
+
+def test_chi2_contingency_trivial():
+    # Some very simple tests for chi2_contingency.
+
+    # A trivial case
+    obs = np.array([[1, 2], [1, 2]])
+    chi2, p, dof, expected = chi2_contingency(obs, correction=False)
+    assert_equal(chi2, 0.0)
+    assert_equal(p, 1.0)
+    assert_equal(dof, 1)
+    assert_array_equal(obs, expected)
+
+    # A *really* trivial case: 1-D data.
+    obs = np.array([1, 2, 3])
+    chi2, p, dof, expected = chi2_contingency(obs, correction=False)
+    assert_equal(chi2, 0.0)
+    assert_equal(p, 1.0)
+    assert_equal(dof, 0)
+    assert_array_equal(obs, expected)
+
+
+def test_chi2_contingency_R():
+    # Some test cases that were computed independently, using R.
+
+    Rcode = \
+    """
+    # Data vector.
+    data <- c(
+      12, 34, 23,     4,  47,  11,
+      35, 31, 11,    34,  10,  18,
+      12, 32,  9,    18,  13,  19,
+      12, 12, 14,     9,  33,  25
+      )
+
+    # Create factor tags:r=rows, c=columns, t=tiers
+    r <- factor(gl(4, 2*3, 2*3*4, labels=c("r1", "r2", "r3", "r4")))
+    c <- factor(gl(3, 1,   2*3*4, labels=c("c1", "c2", "c3")))
+    t <- factor(gl(2, 3,   2*3*4, labels=c("t1", "t2")))
+
+    # 3-way Chi squared test of independence
+    s = summary(xtabs(data~r+c+t))
+    print(s)
+    """
+    Routput = \
+    """
+    Call: xtabs(formula = data ~ r + c + t)
+    Number of cases in table: 478
+    Number of factors: 3
+    Test for independence of all factors:
+            Chisq = 102.17, df = 17, p-value = 3.514e-14
+    """
+    obs = np.array(
+        [[[12, 34, 23],
+          [35, 31, 11],
+          [12, 32, 9],
+          [12, 12, 14]],
+         [[4, 47, 11],
+          [34, 10, 18],
+          [18, 13, 19],
+          [9, 33, 25]]])
+    chi2, p, dof, expected = chi2_contingency(obs)
+    assert_approx_equal(chi2, 102.17, significant=5)
+    assert_approx_equal(p, 3.514e-14, significant=4)
+    assert_equal(dof, 17)
+
+    Rcode = \
+    """
+    # Data vector.
+    data <- c(
+        #
+        12, 17,
+        11, 16,
+        #
+        11, 12,
+        15, 16,
+        #
+        23, 15,
+        30, 22,
+        #
+        14, 17,
+        15, 16
+        )
+
+    # Create factor tags:r=rows, c=columns, d=depths(?), t=tiers
+    r <- factor(gl(2, 2,  2*2*2*2, labels=c("r1", "r2")))
+    c <- factor(gl(2, 1,  2*2*2*2, labels=c("c1", "c2")))
+    d <- factor(gl(2, 4,  2*2*2*2, labels=c("d1", "d2")))
+    t <- factor(gl(2, 8,  2*2*2*2, labels=c("t1", "t2")))
+
+    # 4-way Chi squared test of independence
+    s = summary(xtabs(data~r+c+d+t))
+    print(s)
+    """
+    Routput = \
+    """
+    Call: xtabs(formula = data ~ r + c + d + t)
+    Number of cases in table: 262
+    Number of factors: 4
+    Test for independence of all factors:
+            Chisq = 8.758, df = 11, p-value = 0.6442
+    """
+    obs = np.array(
+        [[[[12, 17],
+           [11, 16]],
+          [[11, 12],
+           [15, 16]]],
+         [[[23, 15],
+           [30, 22]],
+          [[14, 17],
+           [15, 16]]]])
+    chi2, p, dof, expected = chi2_contingency(obs)
+    assert_approx_equal(chi2, 8.758, significant=4)
+    assert_approx_equal(p, 0.6442, significant=4)
+    assert_equal(dof, 11)
+
+
+def test_chi2_contingency_g():
+    c = np.array([[15, 60], [15, 90]])
+    g, p, dof, e = chi2_contingency(c, lambda_='log-likelihood', correction=False)
+    assert_allclose(g, 2*xlogy(c, c/e).sum())
+
+    g, p, dof, e = chi2_contingency(c, lambda_='log-likelihood', correction=True)
+    c_corr = c + np.array([[-0.5, 0.5], [0.5, -0.5]])
+    assert_allclose(g, 2*xlogy(c_corr, c_corr/e).sum())
+
+    c = np.array([[10, 12, 10], [12, 10, 10]])
+    g, p, dof, e = chi2_contingency(c, lambda_='log-likelihood')
+    assert_allclose(g, 2*xlogy(c, c/e).sum())
+
+
+def test_chi2_contingency_bad_args():
+    # Test that "bad" inputs raise a ValueError.
+
+    # Negative value in the array of observed frequencies.
+    obs = np.array([[-1, 10], [1, 2]])
+    assert_raises(ValueError, chi2_contingency, obs)
+
+    # The zeros in this will result in zeros in the array
+    # of expected frequencies.
+    obs = np.array([[0, 1], [0, 1]])
+    assert_raises(ValueError, chi2_contingency, obs)
+
+    # A degenerate case: `observed` has size 0.
+    obs = np.empty((0, 8))
+    assert_raises(ValueError, chi2_contingency, obs)
+
+
+if __name__ == "__main__":
+    run_module_suite()

pywafo/src/wafo/stats/tests/test_continuous_basic.py

@@ -2,11 +2,15 @@ from __future__ import division, print_function, absolute_import
 
 import warnings
 
-import numpy.testing as npt
 import numpy as np
-import nose
+import numpy.testing as npt
 
-from wafo import stats
+from scipy import integrate
+from scipy import stats
+from common_tests import (check_normalization, check_moment, check_mean_expect,
+        check_var_expect, check_skew_expect, check_kurt_expect,
+        check_entropy, check_private_entropy, NUMPY_BELOW_1_7,
+        check_edge_support, check_named_args)
 
 """
 Test all continuous distributions.
@@ -17,39 +21,30 @@ distributions so that we can perform further testing of class methods.
 
 These tests currently check only/mostly for serious errors and exceptions,
 not for numerically exact results.
-
-
-TODO:
-* make functioning test for skew and kurtosis
-  still known failures - skip for now
-
-
 """
 
-#currently not used
+DECIMAL = 5  # specify the precision of the tests  # increased from 0 to 5
-DECIMAL = 5 # specify the precision of the tests  # increased from 0 to 5
-DECIMAL_kurt = 0
 
 distcont = [
     ['alpha', (3.5704770516650459,)],
     ['anglit', ()],
     ['arcsine', ()],
     ['beta', (2.3098496451481823, 0.62687954300963677)],
-    ['betaprime', (5, 6)],   # avoid unbound error in entropy with (100, 86)],
+    ['betaprime', (5, 6)],
     ['bradford', (0.29891359763170633,)],
-    ['burr', (10.5, 4.3)],    #incorrect mean and var for(0.94839838075366045, 4.3820284068855795)],
+    ['burr', (10.5, 4.3)],
     ['cauchy', ()],
     ['chi', (78,)],
     ['chi2', (55,)],
     ['cosine', ()],
     ['dgamma', (1.1023326088288166,)],
     ['dweibull', (2.0685080649914673,)],
-    ['erlang', (20,)],    #correction numargs = 1
+    ['erlang', (10,)],
     ['expon', ()],
     ['exponpow', (2.697119160358469,)],
     ['exponweib', (2.8923945291034436, 1.9505288745913174)],
     ['f', (29, 18)],
-    ['fatiguelife', (29,)],   #correction numargs = 1
+    ['fatiguelife', (29,)],   # correction numargs = 1
     ['fisk', (3.0857548622253179,)],
     ['foldcauchy', (4.7164673455831894,)],
     ['foldnorm', (1.9521253373555869,)],
@@ -57,9 +52,9 @@ distcont = [
     ['frechet_r', (1.8928171603534227,)],
     ['gamma', (1.9932305483800778,)],
     ['gausshyper', (13.763771604130699, 3.1189636648681431,
-                    2.5145980350183019, 5.1811649903971615)],  #veryslow
+                    2.5145980350183019, 5.1811649903971615)],  # veryslow
     ['genexpon', (9.1325976465418908, 16.231956600590632, 3.2819552690843983)],
-    ['genextreme', (-0.1,)],  # sample mean test fails for (3.3184017469423535,)],
+    ['genextreme', (-0.1,)],
     ['gengamma', (4.4162385429431925, 3.1193091679242761)],
     ['genhalflogistic', (0.77274727809929322,)],
     ['genlogistic', (0.41192440799679475,)],
@@ -72,12 +67,12 @@ distcont = [
     ['halflogistic', ()],
     ['halfnorm', ()],
     ['hypsecant', ()],
-    ['invgamma', (2.0668996136993067,)],
+    ['invgamma', (4.0668996136993067,)],
     ['invgauss', (0.14546264555347513,)],
-    ['invweibull', (10.58,)], # sample mean test fails at(0.58847112119264788,)]
+    ['invweibull', (10.58,)],
     ['johnsonsb', (4.3172675099141058, 3.1837781130785063)],
     ['johnsonsu', (2.554395574161155, 2.2482281679651965)],
-    ['ksone', (1000,)],  #replace 22 by 100 to avoid failing range, ticket 956
+    ['ksone', (1000,)],  # replace 22 by 100 to avoid failing range, ticket 956
     ['kstwobign', ()],
     ['laplace', ()],
     ['levy', ()],
@@ -91,8 +86,7 @@ distcont = [
     ['lognorm', (0.95368226960575331,)],
     ['lomax', (1.8771398388773268,)],
     ['maxwell', ()],
-    ['mielke', (10.4, 3.6)], # sample mean test fails for (4.6420495492121487, 0.59707419545516938)],
+    ['mielke', (10.4, 3.6)],
-                             # mielke: good results if 2nd parameter >2, weird mean or var below
     ['nakagami', (4.9673794866666237,)],
     ['ncf', (27, 27, 0.41578441799226107)],
     ['nct', (14, 0.24045031331198066)],
@@ -105,8 +99,6 @@ distcont = [
     ['powernorm', (4.4453652254590779,)],
     ['rayleigh', ()],
     ['rdist', (0.9,)],   # feels also slow
-#    ['rdist', (3.8266985793976525,)],  #veryslow, especially rvs
-    #['rdist', (541.0,)],   # from ticket #758    #veryslow
     ['recipinvgauss', (0.63004267809369119,)],
     ['reciprocal', (0.0062309367010521255, 1.0062309367010522)],
     ['rice', (0.7749725210111873,)],
@@ -115,22 +107,36 @@ distcont = [
     ['triang', (0.15785029824528218,)],
     ['truncexpon', (4.6907725456810478,)],
     ['truncnorm', (-1.0978730080013919, 2.7306754109031979)],
+    ['truncnorm', (0.1, 2.)],
     ['tukeylambda', (3.1321477856738267,)],
     ['uniform', ()],
     ['vonmises', (3.9939042581071398,)],
+    ['vonmises_line', (3.9939042581071398,)],
     ['wald', ()],
     ['weibull_max', (2.8687961709100187,)],
     ['weibull_min', (1.7866166930421596,)],
     ['wrapcauchy', (0.031071279018614728,)]]
 
+## Last four of these fail all around. Need to be checked
+distcont_extra = [
+    ['betaprime', (100, 86)],
+    ['fatiguelife', (5,)],
+    ['mielke', (4.6420495492121487, 0.59707419545516938)],
+    ['invweibull', (0.58847112119264788,)],
+    # burr: sample mean test fails still for c<1
+    ['burr', (0.94839838075366045, 4.3820284068855795)],
+    # genextreme: sample mean test, sf-logsf test fail
+    ['genextreme', (3.3184017469423535,)],
+]
+
+
 # for testing only specific functions
-##distcont = [
+# distcont = [
-##    ['erlang', (20,)],    #correction numargs = 1
 ##    ['fatiguelife', (29,)],   #correction numargs = 1
 ##    ['loggamma', (0.41411931826052117,)]]
 
 # for testing ticket:767
-##distcont = [
+# distcont = [
 ##    ['genextreme', (3.3184017469423535,)],
 ##    ['genextreme', (0.01,)],
 ##    ['genextreme', (0.00001,)],
@@ -138,12 +144,12 @@ distcont = [
 ##    ['genextreme', (-0.01,)]
 ##    ]
 
-##distcont = [['gumbel_l', ()],
+# distcont = [['gumbel_l', ()],
 ##            ['gumbel_r', ()],
 ##            ['norm', ()]
 ##            ]
 
-##distcont = [['norm', ()]]
+# distcont = [['norm', ()]]
 
 distmissing = ['wald', 'gausshyper', 'genexpon', 'rv_continuous',
     'loglaplace', 'rdist', 'semicircular', 'invweibull', 'ksone',
@@ -154,11 +160,14 @@ distmissing = ['wald', 'gausshyper', 'genexpon', 'rv_continuous',
 
 distmiss = [[dist,args] for dist,args in distcont if dist in distmissing]
 distslow = ['rdist', 'gausshyper', 'recipinvgauss', 'ksone', 'genexpon',
-            'vonmises', 'rice', 'mielke', 'semicircular', 'cosine', 'invweibull',
+            'vonmises', 'vonmises_line', 'mielke', 'semicircular',
-            'powerlognorm', 'johnsonsu', 'kstwobign']
+            'cosine', 'invweibull', 'powerlognorm', 'johnsonsu', 'kstwobign']
-#distslow are sorted by speed (very slow to slow)
+# distslow are sorted by speed (very slow to slow)
+
 
+# NB: not needed anymore?
 def _silence_fp_errors(func):
+    # warning: don't apply to test_ functions as is, then those will be skipped
     def wrap(*a, **kw):
         olderr = np.seterr(all='ignore')
         try:
@@ -168,162 +177,183 @@ def _silence_fp_errors(func):
     wrap.__name__ = func.__name__
     return wrap
 
-@_silence_fp_errors
+
 def test_cont_basic():
     # this test skips slow distributions
-    for distname, arg in distcont[:]:
+    with warnings.catch_warnings():
-        if distname in distslow:
+        warnings.filterwarnings('ignore', category=integrate.IntegrationWarning)
-            continue
+        for distname, arg in distcont[:]:
-        distfn = getattr(stats, distname)
+            if distname in distslow:
-        np.random.seed(765456)
+                continue
-        sn = 1000
+            distfn = getattr(stats, distname)
-        rvs = distfn.rvs(size=sn,*arg)
+            np.random.seed(765456)
-        sm = rvs.mean()
+            sn = 500
-        sv = rvs.var()
+            rvs = distfn.rvs(size=sn, *arg)
-        skurt = stats.kurtosis(rvs)
+            sm = rvs.mean()
-        sskew = stats.skew(rvs)
+            sv = rvs.var()
-        m,v = distfn.stats(*arg)
+            m, v = distfn.stats(*arg)
-
+
-        yield check_sample_meanvar_, distfn, arg, m, v, sm, sv, sn, distname + \
+            yield check_sample_meanvar_, distfn, arg, m, v, sm, sv, sn, \
-              'sample mean test'
+                   distname + 'sample mean test'
-        # the sample skew kurtosis test has known failures, not very good distance measure
+            yield check_cdf_ppf, distfn, arg, distname
-        #yield check_sample_skew_kurt, distfn, arg, sskew, skurt, distname
+            yield check_sf_isf, distfn, arg, distname
-        yield check_moment, distfn, arg, m, v, distname
+            yield check_pdf, distfn, arg, distname
-        yield check_cdf_ppf, distfn, arg, distname
+            yield check_pdf_logpdf, distfn, arg, distname
-        yield check_sf_isf, distfn, arg, distname
+            yield check_cdf_logcdf, distfn, arg, distname
-        yield check_pdf, distfn, arg, distname
+            yield check_sf_logsf, distfn, arg, distname
-        if distname in ['wald']:
+            if distname in distmissing:
-            continue
+                alpha = 0.01
-        yield check_pdf_logpdf, distfn, arg, distname
+                yield check_distribution_rvs, distname, arg, alpha, rvs
-        yield check_cdf_logcdf, distfn, arg, distname
+
-        yield check_sf_logsf, distfn, arg, distname
+            locscale_defaults = (0, 1)
-        if distname in distmissing:
+            meths = [distfn.pdf, distfn.logpdf, distfn.cdf, distfn.logcdf,
-            alpha = 0.01
+                     distfn.logsf]
-            yield check_distribution_rvs, distname, arg, alpha, rvs
+            # make sure arguments are within support
+            spec_x = {'frechet_l': -0.5, 'weibull_max': -0.5, 'levy_l': -0.5,
+                      'pareto': 1.5, 'tukeylambda': 0.3}
+            x = spec_x.get(distname, 0.5)
+            yield check_named_args, distfn, x, arg, locscale_defaults, meths
+
+            # Entropy
+            skp = npt.dec.skipif
+            yield check_entropy, distfn, arg, distname
+
+            if distfn.numargs == 0:
+                yield skp(NUMPY_BELOW_1_7)(check_vecentropy), distfn, arg
+            if distfn.__class__._entropy != stats.rv_continuous._entropy:
+                yield check_private_entropy, distfn, arg, stats.rv_continuous
+
+            yield check_edge_support, distfn, arg
+
+            knf = npt.dec.knownfailureif
+            yield knf(distname == 'truncnorm')(check_ppf_private), distfn, \
+                      arg, distname
 
 @npt.dec.slow
 def test_cont_basic_slow():
     # same as above for slow distributions
-    for distname, arg in distcont[:]:
+    with warnings.catch_warnings():
-        if distname not in distslow: continue
+        warnings.filterwarnings('ignore', category=integrate.IntegrationWarning)
-        distfn = getattr(stats, distname)
+        for distname, arg in distcont[:]:
-        np.random.seed(765456)
+            if distname not in distslow:
-        sn = 1000
+                continue
-        rvs = distfn.rvs(size=sn,*arg)
+            distfn = getattr(stats, distname)
-        sm = rvs.mean()
+            np.random.seed(765456)
-        sv = rvs.var()
+            sn = 500
-        skurt = stats.kurtosis(rvs)
+            rvs = distfn.rvs(size=sn,*arg)
-        sskew = stats.skew(rvs)
+            sm = rvs.mean()
-        m,v = distfn.stats(*arg)
+            sv = rvs.var()
-        yield check_sample_meanvar_, distfn, arg, m, v, sm, sv, sn, distname + \
+            m, v = distfn.stats(*arg)
-              'sample mean test'
+            yield check_sample_meanvar_, distfn, arg, m, v, sm, sv, sn, \
-        # the sample skew kurtosis test has known failures, not very good distance measure
+                  distname + 'sample mean test'
-        #yield check_sample_skew_kurt, distfn, arg, sskew, skurt, distname
+            yield check_cdf_ppf, distfn, arg, distname
-        yield check_moment, distfn, arg, m, v, distname
+            yield check_sf_isf, distfn, arg, distname
-        yield check_cdf_ppf, distfn, arg, distname
+            yield check_pdf, distfn, arg, distname
-        yield check_sf_isf, distfn, arg, distname
+            yield check_pdf_logpdf, distfn, arg, distname
-        yield check_pdf, distfn, arg, distname
+            yield check_cdf_logcdf, distfn, arg, distname
-        yield check_pdf_logpdf, distfn, arg, distname
+            yield check_sf_logsf, distfn, arg, distname
-        yield check_cdf_logcdf, distfn, arg, distname
+            # yield check_oth, distfn, arg # is still missing
-        yield check_sf_logsf, distfn, arg, distname
+            if distname in distmissing:
-        #yield check_oth, distfn, arg # is still missing
+                alpha = 0.01
-        if distname in distmissing:
+                yield check_distribution_rvs, distname, arg, alpha, rvs
-            alpha = 0.01
+
-            yield check_distribution_rvs, distname, arg, alpha, rvs
+            locscale_defaults = (0, 1)
-
+            meths = [distfn.pdf, distfn.logpdf, distfn.cdf, distfn.logcdf,
-@_silence_fp_errors
+                     distfn.logsf]
-def check_moment(distfn, arg, m, v, msg):
+            # make sure arguments are within support
-    m1  = distfn.moment(1,*arg)
+            x = 0.5
-    m2  = distfn.moment(2,*arg)
+            if distname == 'invweibull':
-    if not np.isinf(m):
+                arg = (1,)
-        npt.assert_almost_equal(m1, m, decimal=10, err_msg= msg + \
+            elif distname == 'ksone':
-                            ' - 1st moment')
+                arg = (3,)
-    else:                     # or np.isnan(m1),
+            yield check_named_args, distfn, x, arg, locscale_defaults, meths
-        npt.assert_(np.isinf(m1),
+
-               msg + ' - 1st moment -infinite, m1=%s' % str(m1))
+            # Entropy
-        #np.isnan(m1) temporary special treatment for loggamma
+            skp = npt.dec.skipif
-    if not np.isinf(v):
+            ks_cond = distname in ['ksone', 'kstwobign']
-        npt.assert_almost_equal(m2-m1*m1, v, decimal=10, err_msg= msg + \
+            yield skp(ks_cond)(check_entropy), distfn, arg, distname
-                            ' - 2ndt moment')
+
-    else:                     #or np.isnan(m2),
+            if distfn.numargs == 0:
-        npt.assert_(np.isinf(m2),
+                yield skp(NUMPY_BELOW_1_7)(check_vecentropy), distfn, arg
-               msg + ' - 2nd moment -infinite, m2=%s' % str(m2))
+            if distfn.__class__._entropy != stats.rv_continuous._entropy:
-        #np.isnan(m2) temporary special treatment for loggamma
+                yield check_private_entropy, distfn, arg, stats.rv_continuous
-
+
-@_silence_fp_errors
+            yield check_edge_support, distfn, arg
+
+
+@npt.dec.slow
+def test_moments():
+    with warnings.catch_warnings():
+        warnings.filterwarnings('ignore', category=integrate.IntegrationWarning)
+        knf = npt.dec.knownfailureif
+        fail_normalization = set(['vonmises', 'ksone'])
+        fail_higher = set(['vonmises', 'ksone', 'ncf'])
+        for distname, arg in distcont[:]:
+            distfn = getattr(stats, distname)
+            m, v, s, k = distfn.stats(*arg, moments='mvsk')
+            cond1, cond2 = distname in fail_normalization, distname in fail_higher
+            msg = distname + ' fails moments'
+            yield knf(cond1, msg)(check_normalization), distfn, arg, distname
+            yield knf(cond2, msg)(check_mean_expect), distfn, arg, m, distname
+            yield knf(cond2, msg)(check_var_expect), distfn, arg, m, v, distname
+            yield knf(cond2, msg)(check_skew_expect), distfn, arg, m, v, s, \
+                  distname
+            yield knf(cond2, msg)(check_kurt_expect), distfn, arg, m, v, k, \
+                  distname
+            yield check_loc_scale, distfn, arg, m, v, distname
+            yield check_moment, distfn, arg, m, v, distname
+
+
 def check_sample_meanvar_(distfn, arg, m, v, sm, sv, sn, msg):
-    #this did not work, skipped silently by nose
+    # this did not work, skipped silently by nose
-    #check_sample_meanvar, sm, m, msg + 'sample mean test'
-    #check_sample_meanvar, sv, v, msg + 'sample var test'
     if not np.isinf(m):
         check_sample_mean(sm, sv, sn, m)
     if not np.isinf(v):
         check_sample_var(sv, sn, v)
-##    check_sample_meanvar( sm, m, msg + 'sample mean test')
-##    check_sample_meanvar( sv, v, msg + 'sample var test')
 
-def check_sample_mean(sm,v,n, popmean):
-    """
-from stats.stats.ttest_1samp(a, popmean):
-Calculates the t-obtained for the independent samples T-test on ONE group
-of scores a, given a population mean.
 
-Returns: t-value, two-tailed prob
+def check_sample_mean(sm,v,n, popmean):
-"""
+    # from stats.stats.ttest_1samp(a, popmean):
-##    a = asarray(a)
+    # Calculates the t-obtained for the independent samples T-test on ONE group
-##    x = np.mean(a)
+    # of scores a, given a population mean.
-##    v = np.var(a, ddof=1)
+    #
-##    n = len(a)
+    # Returns: t-value, two-tailed prob
     df = n-1
-    svar = ((n-1)*v) / float(df)    #looks redundant
+    svar = ((n-1)*v) / float(df)    # looks redundant
-    t = (sm-popmean)/np.sqrt(svar*(1.0/n))
+    t = (sm-popmean) / np.sqrt(svar*(1.0/n))
-    prob = stats.betai(0.5*df,0.5,df/(df+t*t))
+    prob = stats.betai(0.5*df, 0.5, df/(df+t*t))
+
+    # return t,prob
+    npt.assert_(prob > 0.01, 'mean fail, t,prob = %f, %f, m, sm=%f,%f' %
+            (t, prob, popmean, sm))
 
-    #return t,prob
-    npt.assert_(prob > 0.01, 'mean fail, t,prob = %f, %f, m,sm=%f,%f' % (t,prob,popmean,sm))
 
 def check_sample_var(sv,n, popvar):
-    '''
+    # two-sided chisquare test for sample variance equal to hypothesized variance
-two-sided chisquare test for sample variance equal to hypothesized variance
-    '''
     df = n-1
     chi2 = (n-1)*popvar/float(popvar)
     pval = stats.chisqprob(chi2,df)*2
-    npt.assert_(pval > 0.01, 'var fail, t,pval = %f, %f, v,sv=%f,%f' % (chi2,pval,popvar,sv))
+    npt.assert_(pval > 0.01, 'var fail, t, pval = %f, %f, v, sv=%f, %f' %
+            (chi2,pval,popvar,sv))
 
 
-def check_sample_skew_kurt(distfn, arg, ss, sk, msg):
-    skew,kurt = distfn.stats(moments='sk',*arg)
-##    skew = distfn.stats(moment='s',*arg)[()]
-##    kurt = distfn.stats(moment='k',*arg)[()]
-    check_sample_meanvar( sk, kurt, msg + 'sample kurtosis test')
-    check_sample_meanvar( ss, skew, msg + 'sample skew test')
-
-def check_sample_meanvar(sm,m,msg):
-    if not np.isinf(m) and not np.isnan(m):
-        npt.assert_almost_equal(sm, m, decimal=DECIMAL, err_msg= msg + \
-                                ' - finite moment')
-##    else:
-##        npt.assert_(abs(sm) > 10000), msg='infinite moment, sm = ' + str(sm))
-
-@_silence_fp_errors
 def check_cdf_ppf(distfn,arg,msg):
     values = [0.001, 0.5, 0.999]
     npt.assert_almost_equal(distfn.cdf(distfn.ppf(values, *arg), *arg),
-                            values, decimal=DECIMAL, err_msg= msg + \
+                            values, decimal=DECIMAL, err_msg=msg +
                             ' - cdf-ppf roundtrip')
 
-@_silence_fp_errors
+
 def check_sf_isf(distfn,arg,msg):
     npt.assert_almost_equal(distfn.sf(distfn.isf([0.1,0.5,0.9], *arg), *arg),
-                            [0.1,0.5,0.9], decimal=DECIMAL, err_msg= msg + \
+                            [0.1,0.5,0.9], decimal=DECIMAL, err_msg=msg +
                             ' - sf-isf roundtrip')
     npt.assert_almost_equal(distfn.cdf([0.1,0.9], *arg),
                             1.0-distfn.sf([0.1,0.9], *arg),
-                            decimal=DECIMAL, err_msg= msg + \
+                            decimal=DECIMAL, err_msg=msg +
                             ' - cdf-sf relationship')
 
-@_silence_fp_errors
+
 def check_pdf(distfn, arg, msg):
     # compares pdf at median with numerical derivative of cdf
     median = distfn.ppf(0.5, *arg)
@@ -335,12 +365,12 @@ def check_pdf(distfn, arg, msg):
         pdfv = distfn.pdf(median, *arg)
     cdfdiff = (distfn.cdf(median + eps, *arg) -
                distfn.cdf(median - eps, *arg))/eps/2.0
-    #replace with better diff and better test (more points),
+    # replace with better diff and better test (more points),
-    #actually, this works pretty well
+    # actually, this works pretty well
     npt.assert_almost_equal(pdfv, cdfdiff,
-                decimal=DECIMAL, err_msg= msg + ' - cdf-pdf relationship')
+                decimal=DECIMAL, err_msg=msg + ' - cdf-pdf relationship')
+
 
-@_silence_fp_errors
 def check_pdf_logpdf(distfn, args, msg):
     # compares pdf at several points with the log of the pdf
     points = np.array([0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8])
@@ -351,7 +381,7 @@ def check_pdf_logpdf(distfn, args, msg):
     logpdf = logpdf[np.isfinite(logpdf)]
     npt.assert_almost_equal(np.log(pdf), logpdf, decimal=7, err_msg=msg + " - logpdf-log(pdf) relationship")
 
-@_silence_fp_errors
+
 def check_sf_logsf(distfn, args, msg):
     # compares sf at several points with the log of the sf
     points = np.array([0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8])
@@ -362,7 +392,7 @@ def check_sf_logsf(distfn, args, msg):
     logsf = logsf[np.isfinite(logsf)]
     npt.assert_almost_equal(np.log(sf), logsf, decimal=7, err_msg=msg + " - logsf-log(sf) relationship")
 
-@_silence_fp_errors
+
 def check_cdf_logcdf(distfn, args, msg):
     # compares cdf at several points with the log of the cdf
     points = np.array([0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8])
@@ -374,10 +404,9 @@ def check_cdf_logcdf(distfn, args, msg):
     npt.assert_almost_equal(np.log(cdf), logcdf, decimal=7, err_msg=msg + " - logcdf-log(cdf) relationship")
 
 
-@_silence_fp_errors
 def check_distribution_rvs(dist, args, alpha, rvs):
-    #test from scipy.stats.tests
+    # test from scipy.stats.tests
-    #this version reuses existing random variables
+    # this version reuses existing random variables
     D,pval = stats.kstest(rvs, dist, args=args, N=1000)
     if (pval < alpha):
         D,pval = stats.kstest(dist,'',args=args, N=1000)
@@ -385,6 +414,22 @@ def check_distribution_rvs(dist, args, alpha, rvs):
                "; alpha = " + str(alpha) + "\nargs = " + str(args))
 
 
+def check_vecentropy(distfn, args):
+    npt.assert_equal(distfn.vecentropy(*args), distfn._entropy(*args))
+
+@npt.dec.skipif(NUMPY_BELOW_1_7)
+def check_loc_scale(distfn, arg, m, v, msg):
+    loc, scale = 10.0, 10.0
+    mt, vt = distfn.stats(loc=loc, scale=scale, *arg)
+    npt.assert_allclose(m*scale + loc, mt)
+    npt.assert_allclose(v*scale*scale, vt)
+
+
+def check_ppf_private(distfn, arg, msg):
+    #fails by design for truncnorm self.nb not defined
+    ppfs = distfn._ppf(np.array([0.1, 0.5, 0.9]), *arg)
+    npt.assert_(not np.any(np.isnan(ppfs)), msg + 'ppf private is nan')
+
+
 if __name__ == "__main__":
-    #nose.run(argv=['', __file__])
+    npt.run_module_suite()
-    nose.runmodule(argv=[__file__,'-s'], exit=False)

pywafo/src/wafo/stats/tests/test_discrete_basic.py

@@ -1,268 +1,202 @@
-import numpy.testing as npt
+from __future__ import division, print_function, absolute_import
-import numpy as np
+
-import nose
+import numpy.testing as npt
-
+import numpy as np
-from wafo import stats
+try:
-
+    from scipy.lib.six import xrange
-DECIMAL_meanvar = 0#1  # was 0
+except:
-
+    pass
-distdiscrete = [
+from scipy import stats
-    ['bernoulli',(0.3,)],
+from .common_tests import (check_normalization, check_moment, check_mean_expect,
-    ['binom',    (5, 0.4)],
+        check_var_expect, check_skew_expect, check_kurt_expect,
-    ['boltzmann',(1.4, 19)],
+        check_entropy, check_private_entropy, check_edge_support,
-    ['dlaplace', (0.8,)], #0.5
+        check_named_args)
-    ['geom',     (0.5,)],
+knf = npt.dec.knownfailureif
-    ['hypergeom',(30, 12, 6)],
+
-    ['hypergeom',(21,3,12)],  #numpy.random (3,18,12) numpy ticket:921
+distdiscrete = [
-    ['hypergeom',(21,18,11)],  #numpy.random (18,3,11) numpy ticket:921
+    ['bernoulli',(0.3,)],
-    ['logser',   (0.6,)],  # reenabled, numpy ticket:921
+    ['binom', (5, 0.4)],
-    ['nbinom',   (5, 0.5)],
+    ['boltzmann',(1.4, 19)],
-    ['nbinom',   (0.4, 0.4)], #from tickets: 583
+    ['dlaplace', (0.8,)],  # 0.5
-    ['planck',   (0.51,)],   #4.1
+    ['geom', (0.5,)],
-    ['poisson',  (0.6,)],
+    ['hypergeom',(30, 12, 6)],
-    ['randint',  (7, 31)],
+    ['hypergeom',(21,3,12)],  # numpy.random (3,18,12) numpy ticket:921
-    ['skellam',  (15, 8)]]
+    ['hypergeom',(21,18,11)],  # numpy.random (18,3,11) numpy ticket:921
-#    ['zipf',     (4,)] ]   # arg=4 is ok,
+    ['logser', (0.6,)],  # reenabled, numpy ticket:921
-                           # Zipf broken for arg = 2, e.g. weird .stats
+    ['nbinom', (5, 0.5)],
-                           # looking closer, mean, var should be inf for arg=2
+    ['nbinom', (0.4, 0.4)],  # from tickets: 583
-
+    ['planck', (0.51,)],   # 4.1
-
+    ['poisson', (0.6,)],
-#@npt.dec.slow
+    ['randint', (7, 31)],
-def test_discrete_basic():
+    ['skellam', (15, 8)],
-    for distname, arg in distdiscrete:
+    ['zipf', (6.5,)]
-        distfn = getattr(stats,distname)
+]
-        #assert stats.dlaplace.rvs(0.8) is not None
+
-        np.random.seed(9765456)
+
-        rvs = distfn.rvs(size=2000,*arg)
+def test_discrete_basic():
-        supp = np.unique(rvs)
+    for distname, arg in distdiscrete:
-        m,v = distfn.stats(*arg)
+        distfn = getattr(stats, distname)
-        #yield npt.assert_almost_equal(rvs.mean(), m, decimal=4,err_msg='mean')
+        np.random.seed(9765456)
-        #yield npt.assert_almost_equal, rvs.mean(), m, 2, 'mean' # does not work
+        rvs = distfn.rvs(size=2000, *arg)
-        yield check_sample_meanvar, rvs.mean(), m, distname + ' sample mean test'
+        supp = np.unique(rvs)
-        yield check_sample_meanvar, rvs.var(), v, distname + ' sample var test'
+        m, v = distfn.stats(*arg)
-        yield check_cdf_ppf, distfn, arg, distname + ' cdf_ppf'
+        yield check_cdf_ppf, distfn, arg, supp, distname + ' cdf_ppf'
-        yield check_cdf_ppf2, distfn, arg, supp, distname + ' cdf_ppf'
+
-        yield check_pmf_cdf, distfn, arg, distname + ' pmf_cdf'
+        yield check_pmf_cdf, distfn, arg, distname
-
+        yield check_oth, distfn, arg, supp, distname + ' oth'
-        # zipf doesn't fail, but generates floating point warnings.
+        yield check_edge_support, distfn, arg
-        # Should be checked.
+
-        if not distname in ['zipf']:
+        alpha = 0.01
-            yield check_oth, distfn, arg, distname + ' oth'
+        yield check_discrete_chisquare, distfn, arg, rvs, alpha, \
-            skurt = stats.kurtosis(rvs)
+                      distname + ' chisquare'
-            sskew = stats.skew(rvs)
+
-            yield check_sample_skew_kurt, distfn, arg, skurt, sskew, \
+    seen = set()
-                          distname + ' skew_kurt'
+    for distname, arg in distdiscrete:
-
+        if distname in seen:
-        # dlaplace doesn't fail, but generates lots of floating point warnings.
+            continue
-        # Should be checked.
+        seen.add(distname)
-        if not distname in ['dlaplace']: #['logser']:  #known failure, fixed
+        distfn = getattr(stats,distname)
-            alpha = 0.01
+        locscale_defaults = (0,)
-            yield check_discrete_chisquare, distfn, arg, rvs, alpha, \
+        meths = [distfn.pmf, distfn.logpmf, distfn.cdf, distfn.logcdf,
-                          distname + ' chisquare'
+                 distfn.logsf]
-
+        # make sure arguments are within support
-@npt.dec.slow
+        spec_k = {'randint': 11, 'hypergeom': 4, 'bernoulli': 0, }
-def test_discrete_extra():
+        k = spec_k.get(distname, 1)
-    for distname, arg in distdiscrete:
+        yield check_named_args, distfn, k, arg, locscale_defaults, meths
-        distfn = getattr(stats,distname)
+        yield check_scale_docstring, distfn
-        yield check_ppf_limits, distfn, arg, distname + \
+
-              ' ppf limit test'
+        # Entropy
-        yield check_isf_limits, distfn, arg, distname + \
+        yield check_entropy, distfn, arg, distname
-              ' isf limit test'
+        if distfn.__class__._entropy != stats.rv_discrete._entropy:
-        yield check_entropy, distfn, arg, distname + \
+            yield check_private_entropy, distfn, arg, stats.rv_discrete
-              ' entropy nan test'
+
-
+
-@npt.dec.skipif(True)
+def test_moments():
-def test_discrete_private():
+    for distname, arg in distdiscrete:
-    #testing private methods mostly for debugging
+        distfn = getattr(stats,distname)
-    #   some tests might fail by design,
+        m, v, s, k = distfn.stats(*arg, moments='mvsk')
-    #   e.g. incorrect definition of distfn.a and distfn.b
+        yield check_normalization, distfn, arg, distname
-    for distname, arg in distdiscrete:
+
-        distfn = getattr(stats,distname)
+        # compare `stats` and `moment` methods
-        rvs = distfn.rvs(size=10000,*arg)
+        yield check_moment, distfn, arg, m, v, distname
-        m,v = distfn.stats(*arg)
+        yield check_mean_expect, distfn, arg, m, distname
-
+        yield check_var_expect, distfn, arg, m, v, distname
-        yield check_ppf_ppf, distfn, arg
+        yield check_skew_expect, distfn, arg, m, v, s, distname
-        yield check_cdf_ppf_private, distfn, arg, distname
+
-        yield check_generic_moment, distfn, arg, m, 1, 3   # last is decimal
+        cond = distname in ['zipf']
-        yield check_generic_moment, distfn, arg, v+m*m, 2, 3 # last is decimal
+        msg = distname + ' fails kurtosis'
-        yield check_moment_frozen, distfn, arg, m, 1, 3   # last is decimal
+        yield knf(cond, msg)(check_kurt_expect), distfn, arg, m, v, k, distname
-        yield check_moment_frozen, distfn, arg, v+m*m, 2, 3 # last is decimal
+
-
+        # frozen distr moments
-
+        yield check_moment_frozen, distfn, arg, m, 1
-def check_sample_meanvar(sm,m,msg):
+        yield check_moment_frozen, distfn, arg, v+m*m, 2
-    if not np.isinf(m):
+
-        npt.assert_almost_equal(sm, m, decimal=DECIMAL_meanvar, err_msg=msg + \
+
-                                ' - finite moment')
+def check_cdf_ppf(distfn, arg, supp, msg):
-    else:
+    # cdf is a step function, and ppf(q) = min{k : cdf(k) >= q, k integer}
-        npt.assert_(sm > 10000, msg='infinite moment, sm = ' + str(sm))
+    npt.assert_array_equal(distfn.ppf(distfn.cdf(supp, *arg), *arg),
-
+                           supp, msg + '-roundtrip')
-def check_sample_var(sm,m,msg):
+    npt.assert_array_equal(distfn.ppf(distfn.cdf(supp, *arg) - 1e-8, *arg),
-    npt.assert_almost_equal(sm, m, decimal=DECIMAL_meanvar, err_msg= msg + 'var')
+                           supp, msg + '-roundtrip')
-
+    supp1 = supp[supp < distfn.b]
-def check_cdf_ppf(distfn,arg,msg):
+    npt.assert_array_equal(distfn.ppf(distfn.cdf(supp1, *arg) + 1e-8, *arg),
-    ppf05 = distfn.ppf(0.5,*arg)
+                     supp1 + distfn.inc, msg + 'ppf-cdf-next')
-    cdf05 = distfn.cdf(ppf05,*arg)
+    # -1e-8 could cause an error if pmf < 1e-8
-    npt.assert_almost_equal(distfn.ppf(cdf05-1e-6,*arg),ppf05,
+
-                            err_msg=msg + 'ppf-cdf-median')
+
-    npt.assert_((distfn.ppf(cdf05+1e-4,*arg)>ppf05), msg + 'ppf-cdf-next')
+def check_pmf_cdf(distfn, arg, distname):
-
+    startind = np.int(distfn.ppf(0.01, *arg) - 1)
-def check_cdf_ppf2(distfn,arg,supp,msg):
+    index = list(range(startind, startind + 10))
-    npt.assert_array_equal(distfn.ppf(distfn.cdf(supp,*arg),*arg),
+    cdfs, pmfs_cum = distfn.cdf(index,*arg), distfn.pmf(index, *arg).cumsum()
-                           supp, msg + '-roundtrip')
+
-    npt.assert_array_equal(distfn.ppf(distfn.cdf(supp,*arg)-1e-8,*arg),
+    atol, rtol = 1e-10, 1e-10
-                           supp, msg + '-roundtrip')
+    if distname == 'skellam':    # ncx2 accuracy
-    # -1e-8 could cause an error if pmf < 1e-8
+        atol, rtol = 1e-5, 1e-5
-
+    npt.assert_allclose(cdfs - cdfs[0], pmfs_cum - pmfs_cum[0],
-
+            atol=atol, rtol=rtol)
-def check_cdf_ppf_private(distfn,arg,msg):
+
-    ppf05 = distfn._ppf(0.5,*arg)
+
-    cdf05 = distfn.cdf(ppf05,*arg)
+def check_moment_frozen(distfn, arg, m, k):
-    npt.assert_almost_equal(distfn._ppf(cdf05-1e-6,*arg),ppf05,
+    npt.assert_allclose(distfn(*arg).moment(k), m,
-                            err_msg=msg + '_ppf-cdf-median ')
+            atol=1e-10, rtol=1e-10)
-    npt.assert_((distfn._ppf(cdf05+1e-4,*arg)>ppf05), msg + '_ppf-cdf-next')
+
-
+
-def check_ppf_ppf(distfn, arg):
+def check_oth(distfn, arg, supp, msg):
-    npt.assert_(distfn.ppf(0.5,*arg) < np.inf)
+    # checking other methods of distfn
-    ppfs = distfn.ppf([0.5,0.9],*arg)
+    npt.assert_allclose(distfn.sf(supp, *arg), 1. - distfn.cdf(supp, *arg),
-    ppf_s = [distfn._ppf(0.5,*arg), distfn._ppf(0.9,*arg)]
+            atol=1e-10, rtol=1e-10)
-    npt.assert_(np.all(ppfs < np.inf))
+
-    npt.assert_(ppf_s[0] == distfn.ppf(0.5,*arg))
+    q = np.linspace(0.01, 0.99, 20)
-    npt.assert_(ppf_s[1] == distfn.ppf(0.9,*arg))
+    npt.assert_allclose(distfn.isf(q, *arg), distfn.ppf(1. - q, *arg),
-    npt.assert_(ppf_s[0] == ppfs[0])
+            atol=1e-10, rtol=1e-10)
-    npt.assert_(ppf_s[1] == ppfs[1])
+
-
+    median_sf = distfn.isf(0.5, *arg)
-def check_pmf_cdf(distfn, arg, msg):
+    npt.assert_(distfn.sf(median_sf - 1, *arg) > 0.5)
-    startind = np.int(distfn._ppf(0.01,*arg)-1)
+    npt.assert_(distfn.cdf(median_sf + 1, *arg) > 0.5)
-    index = range(startind,startind+10)
+
-    cdfs = distfn.cdf(index,*arg)
+
-    npt.assert_almost_equal(cdfs, distfn.pmf(index, *arg).cumsum() + \
+def check_discrete_chisquare(distfn, arg, rvs, alpha, msg):
-                            cdfs[0] - distfn.pmf(index[0],*arg),
+    """Perform chisquare test for random sample of a discrete distribution
-                            decimal=4, err_msg= msg + 'pmf-cdf')
+
-
+    Parameters
-def check_generic_moment(distfn, arg, m, k, decim):
+    ----------
-    npt.assert_almost_equal(distfn.generic_moment(k,*arg), m, decimal=decim,
+    distname : string
-                            err_msg= str(distfn) + ' generic moment test')
+        name of distribution function
-
+    arg : sequence
-def check_moment_frozen(distfn, arg, m, k, decim):
+        parameters of distribution
-    npt.assert_almost_equal(distfn(*arg).moment(k), m, decimal=decim,
+    alpha : float
-                            err_msg= str(distfn) + ' frozen moment test')
+        significance level, threshold for p-value
-
+
-def check_oth(distfn, arg, msg):
+    Returns
-    #checking other methods of distfn
+    -------
-    meanint = round(float(distfn.stats(*arg)[0])) # closest integer to mean
+    result : bool
-    npt.assert_almost_equal(distfn.sf(meanint, *arg), 1 - \
+        0 if test passes, 1 if test fails
-                            distfn.cdf(meanint, *arg), decimal=8)
+
-    median_sf = distfn.isf(0.5, *arg)
+    uses global variable debug for printing results
-
+
-    npt.assert_(distfn.sf(median_sf - 1, *arg) > 0.5)
+    """
-    npt.assert_(distfn.cdf(median_sf + 1, *arg) > 0.5)
+    n = len(rvs)
-    npt.assert_equal(distfn.isf(0.5, *arg), distfn.ppf(0.5, *arg))
+    nsupp = 20
-
+    wsupp = 1.0/nsupp
-#next 3 functions copied from test_continous_extra
+
-#    adjusted
+    # construct intervals with minimum mass 1/nsupp
-
+    # intervals are left-half-open as in a cdf difference
-def check_ppf_limits(distfn,arg,msg):
+    distsupport = xrange(max(distfn.a, -1000), min(distfn.b, 1000) + 1)
-    below,low,upp,above = distfn.ppf([-1,0,1,2], *arg)
+    last = 0
-    #print distfn.name, distfn.a, low, distfn.b, upp
+    distsupp = [max(distfn.a, -1000)]
-    #print distfn.name,below,low,upp,above
+    distmass = []
-    assert_equal_inf_nan(distfn.a-1,low, msg + 'ppf lower bound')
+    for ii in distsupport:
-    assert_equal_inf_nan(distfn.b,upp, msg + 'ppf upper bound')
+        current = distfn.cdf(ii,*arg)
-    npt.assert_(np.isnan(below), msg + 'ppf out of bounds - below')
+        if current - last >= wsupp-1e-14:
-    npt.assert_(np.isnan(above), msg + 'ppf out of bounds - above')
+            distsupp.append(ii)
-
+            distmass.append(current - last)
-def check_isf_limits(distfn,arg,msg):
+            last = current
-    below,low,upp,above = distfn.isf([-1,0,1,2], *arg)
+            if current > (1-wsupp):
-    #print distfn.name, distfn.a, low, distfn.b, upp
+                break
-    #print distfn.name,below,low,upp,above
+    if distsupp[-1] < distfn.b:
-    assert_equal_inf_nan(distfn.a-1,upp, msg + 'isf lower bound')
+        distsupp.append(distfn.b)
-    assert_equal_inf_nan(distfn.b,low, msg + 'isf upper bound')
+        distmass.append(1-last)
-    npt.assert_(np.isnan(below), msg + 'isf out of bounds - below')
+    distsupp = np.array(distsupp)
-    npt.assert_(np.isnan(above), msg + 'isf out of bounds - above')
+    distmass = np.array(distmass)
-
+
-def assert_equal_inf_nan(v1,v2,msg):
+    # convert intervals to right-half-open as required by histogram
-    npt.assert_(not np.isnan(v1))
+    histsupp = distsupp+1e-8
-    if not np.isinf(v1):
+    histsupp[0] = distfn.a
-        npt.assert_almost_equal(v1, v2, decimal=10, err_msg = msg + \
+
-                                   ' - finite')
+    # find sample frequencies and perform chisquare test
-    else:
+    freq,hsupp = np.histogram(rvs,histsupp)
-        npt.assert_(np.isinf(v2) or np.isnan(v2),
+    cdfs = distfn.cdf(distsupp,*arg)
-               msg + ' - infinite, v2=%s' % str(v2))
+    (chis,pval) = stats.chisquare(np.array(freq),n*distmass)
-
+
-def check_sample_skew_kurt(distfn, arg, sk, ss, msg):
+    npt.assert_(pval > alpha, 'chisquare - test for %s'
-    k,s = distfn.stats(moment='ks',*arg)
+           ' at arg = %s with pval = %s' % (msg,str(arg),str(pval)))
-    check_sample_meanvar, sk, k, msg + 'sample skew test'
+
-    check_sample_meanvar, ss, s, msg + 'sample kurtosis test'
+
-
+def check_scale_docstring(distfn):
-
+    if distfn.__doc__ is not None:
-def check_entropy(distfn,arg,msg):
+        # Docstrings can be stripped if interpreter is run with -OO
-    ent = distfn.entropy(*arg)
+        npt.assert_('scale' not in distfn.__doc__)
-    #print 'Entropy =', ent
+
-    npt.assert_(not np.isnan(ent), msg + 'test Entropy is nan')
+
-
+if __name__ == "__main__":
-
+    npt.run_module_suite()
-def check_discrete_chisquare(distfn, arg, rvs, alpha, msg):
-    '''perform chisquare test for random sample of a discrete distribution
-
-    Parameters
-    ----------
-    distname : string
-        name of distribution function
-    arg : sequence
-        parameters of distribution
-    alpha : float
-        significance level, threshold for p-value
-
-    Returns
-    -------
-    result : bool
-        0 if test passes, 1 if test fails
-
-    uses global variable debug for printing results
-    '''
-
-    # define parameters for test
-##    n=2000
-    n = len(rvs)
-    nsupp = 20
-    wsupp = 1.0/nsupp
-
-##    distfn = getattr(stats, distname)
-##    np.random.seed(9765456)
-##    rvs = distfn.rvs(size=n,*arg)
-
-    # construct intervals with minimum mass 1/nsupp
-    # intervalls are left-half-open as in a cdf difference
-    distsupport = xrange(max(distfn.a, -1000), min(distfn.b, 1000) + 1)
-    last = 0
-    distsupp = [max(distfn.a, -1000)]
-    distmass = []
-    for ii in distsupport:
-        current = distfn.cdf(ii,*arg)
-        if  current - last >= wsupp-1e-14:
-            distsupp.append(ii)
-            distmass.append(current - last)
-            last = current
-            if current > (1-wsupp):
-                break
-    if distsupp[-1]  < distfn.b:
-        distsupp.append(distfn.b)
-        distmass.append(1-last)
-    distsupp = np.array(distsupp)
-    distmass = np.array(distmass)
-
-    # convert intervals to right-half-open as required by histogram
-    histsupp = distsupp+1e-8
-    histsupp[0] = distfn.a
-
-    # find sample frequencies and perform chisquare test
-    freq,hsupp = np.histogram(rvs,histsupp)
-    cdfs = distfn.cdf(distsupp,*arg)
-    (chis,pval) = stats.chisquare(np.array(freq),n*distmass)
-
-    npt.assert_(pval > alpha, 'chisquare - test for %s'
-           ' at arg = %s with pval = %s' % (msg,str(arg),str(pval)))
-
-
-if __name__ == "__main__":
-    #nose.run(argv=['', __file__])
-    nose.runmodule(argv=[__file__,'-s'], exit=False)

pywafo/src/wafo/stats/tests/test_fit.py

@@ -1,98 +1,100 @@
-# NOTE: contains only one test, _est_cont_fit, that is renamed so that
-#       nose doesn't run it
-# I put this here for the record and for the case when someone wants to
-# verify the quality of fit
-# with current parameters: relatively small sample size, default starting values
-#       Ran 84 tests in 401.797s
-#       FAILED (failures=15)
-#
-#Ran 83 tests in 238.859s
-#FAILED (failures=12)
-
 from __future__ import division, print_function, absolute_import
 
-import numpy.testing as npt
+import os
+
 import numpy as np
+from numpy.testing import dec
 
 from wafo import stats
 
-from test_continuous_basic import distcont
+from .test_continuous_basic import distcont
 
 # this is not a proper statistical test for convergence, but only
 # verifies that the estimate and true values don't differ by too much
-n_repl1 = 1000 # sample size for first run
+
-n_repl2 = 5000 # sample size for second run, if first run fails
+fit_sizes = [1000, 5000]  # sample sizes to try
-thresh_percent = 0.25 # percent of true parameters for fail cut-off
+thresh_percent = 0.25  # percent of true parameters for fail cut-off
 thresh_min = 0.75  # minimum difference estimate - true to fail test
 
+failing_fits = [
+        'burr',
+        'chi',
+        'chi2',
+        'gausshyper',
+        'genexpon',
+        'gengamma',
+        'ksone',
+        'mielke',
+        'ncf',
+        'ncx2',
+        'pearson3',
+        'powerlognorm',
+        'truncexpon',
+        'tukeylambda',
+        'vonmises',
+        'wrapcauchy',
+]
 
-distslow = [ 'ncx2', 'rdist', 'gausshyper', 'recipinvgauss', 'ksone', 'genexpon',
+# Don't run the fit test on these:
-            'vonmises', 'rice', 'mielke',
+skip_fit = [
-            'powerlognorm', 'kstwobign', 'tukeylambda','betaprime', 'gengamma', 
+    'erlang',  # Subclass of gamma, generates a warning.
-             'johnsonsb', 'burr', 'truncexpon', 'pearson3', 'exponweib', 'nakagami', 
+]
-             'wrapcauchy']
-dist_rarely_fitted = ['f', 'ncf', 'nct', 'chi']
-distskip = distslow + dist_rarely_fitted    
 
-#distcont = [['genextreme', (3.3184017469423535,)]]
-#@npt.dec.slow
-def test_cont_fit():
-    # this tests the closeness of the estimated parameters to the true
-    # parameters with fit method of continuous distributions 
-    for distname, arg in distcont:
-        if distname not in distskip:
-            yield check_cont_fit, distname,arg
 
-@npt.dec.slow
+@dec.slow
-def _est_cont_fit_slow():
+def test_cont_fit():
     # this tests the closeness of the estimated parameters to the true
     # parameters with fit method of continuous distributions
     # Note: is slow, some distributions don't converge with sample size <= 10000
+
     for distname, arg in distcont:
-        if distname in distslow:
+        if distname not in skip_fit:
             yield check_cont_fit, distname,arg
 
-def test_lognorm_fit_ticket1131():
-    params = [(2.1, 1.,1.), (1.,10.,1.), (1.,1.,10.)]
-    for param in params:
-        yield check_cont_fit, 'lognorm', param
 
-def check_cont_fit(distname,arg):        
+def check_cont_fit(distname,arg):
+    if distname in failing_fits:
+        # Skip failing fits unless overridden
+        xfail = True
+        try:
+            xfail = not int(os.environ['SCIPY_XFAIL'])
+        except:
+            pass
+        if xfail:
+            msg = "Fitting %s doesn't work reliably yet" % distname
+            msg += " [Set environment variable SCIPY_XFAIL=1 to run this test nevertheless.]"
+            dec.knownfailureif(True, msg)(lambda: None)()
+
     distfn = getattr(stats, distname)
-    rvs = distfn.rvs(size=n_repl1,*arg)
+
-    est = distfn.fit(rvs) #, *arg) # start with default values
+    truearg = np.hstack([arg,[0.0,1.0]])
-    n = distfn.numargs + 2
-    truearg = np.hstack([arg,[0.0, 1.0]])[:n]
-    
-    diff = est-truearg
-        
-    txt = ''
     diffthreshold = np.max(np.vstack([truearg*thresh_percent,
-                    np.ones(distfn.numargs+2)*thresh_min]),0)
+                                      np.ones(distfn.numargs+2)*thresh_min]),0)
-    # threshold for location
+
-    diffthreshold[-2] = np.max([np.abs(rvs.mean())*thresh_percent,thresh_min])
+    for fit_size in fit_sizes:
-    
+        # Note that if a fit succeeds, the other fit_sizes are skipped
-    if np.any(np.isnan(est)):
+        np.random.seed(1234)
-        raise AssertionError('nan returned in fit')
+
+        with np.errstate(all='ignore'):
+            rvs = distfn.rvs(size=fit_size, *arg)
+            est = distfn.fit(rvs)  # start with default values
+
+        diff = est - truearg
+
+        # threshold for location
+        diffthreshold[-2] = np.max([np.abs(rvs.mean())*thresh_percent,thresh_min])
+
+        if np.any(np.isnan(est)):
+            raise AssertionError('nan returned in fit')
+        else:
+            if np.all(np.abs(diff) <= diffthreshold):
+                break
     else:
-        if np.any((np.abs(diff) - diffthreshold) > 0.0):
+        txt = 'parameter: %s\n' % str(truearg)
-##            txt = 'WARNING - diff too large with small sample'
+        txt += 'estimated: %s\n' % str(est)
-##            print 'parameter diff =', diff - diffthreshold, txt
+        txt += 'diff     : %s\n' % str(diff)
-            rvs = np.concatenate([rvs,distfn.rvs(size=n_repl2-n_repl1,*arg)])
+        raise AssertionError('fit not very good in %s\n' % distfn.name + txt)
-            est = distfn.fit(rvs) #,*arg)
+
-            truearg = np.hstack([arg,[0.0,1.0]])[:n]
+
-            diff = est-truearg
+if __name__ == "__main__":
-            if np.any((np.abs(diff) - diffthreshold) > 0.0):
+    np.testing.run_module_suite()
-                txt  = 'parameter: %s\n' % str(truearg)
-                txt += 'estimated: %s\n' % str(est)
-                txt += 'diff     : %s\n' % str(diff)
-                raise AssertionError('fit not very good in %s\n' % distfn.name + txt)
-
-
-if __name__ == "__main__":    
-    check_cont_fit('bradford', (0.29891359763170633,))
-#    check_cont_fit('lognorm', (10,1,1))
-#    check_cont_fit('ncx2', (21, 1.0560465975116415))
-    import nose
-    #nose.run(argv=['', __file__])
-    nose.runmodule(argv=[__file__,'-s'], exit=False)

pywafo/src/wafo/stats/tests/test_kdeoth.py

@@ -1,9 +1,10 @@
-
+from __future__ import division, print_function, absolute_import
-
 
 from wafo import stats
 import numpy as np
-from numpy.testing import assert_almost_equal, assert_
+from numpy.testing import assert_almost_equal, assert_, assert_raises, \
+    assert_array_almost_equal, assert_array_almost_equal_nulp, run_module_suite
+
 
 def test_kde_1d():
     #some basic tests comparing to normal distribution
@@ -15,13 +16,13 @@ def test_kde_1d():
 
     # get kde for original sample
     gkde = stats.gaussian_kde(xn)
-    
+
-    # evaluate the density funtion for the kde for some points
+    # evaluate the density function for the kde for some points
     xs = np.linspace(-7,7,501)
     kdepdf = gkde.evaluate(xs)
     normpdf = stats.norm.pdf(xs, loc=xnmean, scale=xnstd)
     intervall = xs[1] - xs[0]
-    
+
     assert_(np.sum((kdepdf - normpdf)**2)*intervall < 0.01)
     prob1 = gkde.integrate_box_1d(xnmean, np.inf)
     prob2 = gkde.integrate_box_1d(-np.inf, xnmean)
@@ -29,8 +30,155 @@ def test_kde_1d():
     assert_almost_equal(prob2, 0.5, decimal=1)
     assert_almost_equal(gkde.integrate_box(xnmean, np.inf), prob1, decimal=13)
     assert_almost_equal(gkde.integrate_box(-np.inf, xnmean), prob2, decimal=13)
-    
+
     assert_almost_equal(gkde.integrate_kde(gkde),
                         (kdepdf**2).sum()*intervall, decimal=2)
     assert_almost_equal(gkde.integrate_gaussian(xnmean, xnstd**2),
-                        (kdepdf*normpdf).sum()*intervall, decimal=2) 
+                        (kdepdf*normpdf).sum()*intervall, decimal=2)
+
+
+def test_kde_bandwidth_method():
+    def scotts_factor(kde_obj):
+        """Same as default, just check that it works."""
+        return np.power(kde_obj.n, -1./(kde_obj.d+4))
+
+    np.random.seed(8765678)
+    n_basesample = 50
+    xn = np.random.randn(n_basesample)
+
+    # Default
+    gkde = stats.gaussian_kde(xn)
+    # Supply a callable
+    gkde2 = stats.gaussian_kde(xn, bw_method=scotts_factor)
+    # Supply a scalar
+    gkde3 = stats.gaussian_kde(xn, bw_method=gkde.factor)
+
+    xs = np.linspace(-7,7,51)
+    kdepdf = gkde.evaluate(xs)
+    kdepdf2 = gkde2.evaluate(xs)
+    assert_almost_equal(kdepdf, kdepdf2)
+    kdepdf3 = gkde3.evaluate(xs)
+    assert_almost_equal(kdepdf, kdepdf3)
+
+    assert_raises(ValueError, stats.gaussian_kde, xn, bw_method='wrongstring')
+
+
+# Subclasses that should stay working (extracted from various sources).
+# Unfortunately the earlier design of gaussian_kde made it necessary for users
+# to create these kinds of subclasses, or call _compute_covariance() directly.
+
+class _kde_subclass1(stats.gaussian_kde):
+    def __init__(self, dataset):
+        self.dataset = np.atleast_2d(dataset)
+        self.d, self.n = self.dataset.shape
+        self.covariance_factor = self.scotts_factor
+        self._compute_covariance()
+
+
+class _kde_subclass2(stats.gaussian_kde):
+    def __init__(self, dataset):
+        self.covariance_factor = self.scotts_factor
+        super(_kde_subclass2, self).__init__(dataset)
+
+
+class _kde_subclass3(stats.gaussian_kde):
+    def __init__(self, dataset, covariance):
+        self.covariance = covariance
+        stats.gaussian_kde.__init__(self, dataset)
+
+    def _compute_covariance(self):
+        self.inv_cov = np.linalg.inv(self.covariance)
+        self._norm_factor = np.sqrt(np.linalg.det(2*np.pi * self.covariance)) \
+                                   * self.n
+
+
+class _kde_subclass4(stats.gaussian_kde):
+    def covariance_factor(self):
+        return 0.5 * self.silverman_factor()
+
+
+def test_gaussian_kde_subclassing():
+    x1 = np.array([-7, -5, 1, 4, 5], dtype=np.float)
+    xs = np.linspace(-10, 10, num=50)
+
+    # gaussian_kde itself
+    kde = stats.gaussian_kde(x1)
+    ys = kde(xs)
+
+    # subclass 1
+    kde1 = _kde_subclass1(x1)
+    y1 = kde1(xs)
+    assert_array_almost_equal_nulp(ys, y1, nulp=10)
+
+    # subclass 2
+    kde2 = _kde_subclass2(x1)
+    y2 = kde2(xs)
+    assert_array_almost_equal_nulp(ys, y2, nulp=10)
+
+    # subclass 3
+    kde3 = _kde_subclass3(x1, kde.covariance)
+    y3 = kde3(xs)
+    assert_array_almost_equal_nulp(ys, y3, nulp=10)
+
+    # subclass 4
+    kde4 = _kde_subclass4(x1)
+    y4 = kde4(x1)
+    y_expected = [0.06292987, 0.06346938, 0.05860291, 0.08657652, 0.07904017]
+
+    assert_array_almost_equal(y_expected, y4, decimal=6)
+
+    # Not a subclass, but check for use of _compute_covariance()
+    kde5 = kde
+    kde5.covariance_factor = lambda: kde.factor
+    kde5._compute_covariance()
+    y5 = kde5(xs)
+    assert_array_almost_equal_nulp(ys, y5, nulp=10)
+
+
+def test_gaussian_kde_covariance_caching():
+    x1 = np.array([-7, -5, 1, 4, 5], dtype=np.float)
+    xs = np.linspace(-10, 10, num=5)
+    # These expected values are from scipy 0.10, before some changes to
+    # gaussian_kde.  They were not compared with any external reference.
+    y_expected = [0.02463386, 0.04689208, 0.05395444, 0.05337754, 0.01664475]
+
+    # Set the bandwidth, then reset it to the default.
+    kde = stats.gaussian_kde(x1)
+    kde.set_bandwidth(bw_method=0.5)
+    kde.set_bandwidth(bw_method='scott')
+    y2 = kde(xs)
+
+    assert_array_almost_equal(y_expected, y2, decimal=7)
+
+
+def test_gaussian_kde_monkeypatch():
+    """Ugly, but people may rely on this.  See scipy pull request 123,
+    specifically the linked ML thread "Width of the Gaussian in stats.kde".
+    If it is necessary to break this later on, that is to be discussed on ML.
+    """
+    x1 = np.array([-7, -5, 1, 4, 5], dtype=np.float)
+    xs = np.linspace(-10, 10, num=50)
+
+    # The old monkeypatched version to get at Silverman's Rule.
+    kde = stats.gaussian_kde(x1)
+    kde.covariance_factor = kde.silverman_factor
+    kde._compute_covariance()
+    y1 = kde(xs)
+
+    # The new saner version.
+    kde2 = stats.gaussian_kde(x1, bw_method='silverman')
+    y2 = kde2(xs)
+
+    assert_array_almost_equal_nulp(y1, y2, nulp=10)
+
+
+def test_kde_integer_input():
+    """Regression test for #1181."""
+    x1 = np.arange(5)
+    kde = stats.gaussian_kde(x1)
+    y_expected = [0.13480721, 0.18222869, 0.19514935, 0.18222869, 0.13480721]
+    assert_array_almost_equal(kde(x1), y_expected, decimal=6)
+
+
+if __name__ == "__main__":
+    run_module_suite()

pywafo/src/wafo/stats/tests/test_morestats.py

@@ -0,0 +1,789 @@
+# Author:  Travis Oliphant, 2002
+#
+# Further enhancements and tests added by numerous SciPy developers.
+#
+from __future__ import division, print_function, absolute_import
+
+import warnings
+
+import numpy as np
+from numpy.random import RandomState
+from numpy.testing import (TestCase, run_module_suite, assert_array_equal,
+    assert_almost_equal, assert_array_less, assert_array_almost_equal,
+    assert_raises, assert_, assert_allclose, assert_equal, dec)
+
+from scipy import stats
+
+# Matplotlib is not a scipy dependency but is optionally used in probplot, so
+# check if it's available
+try:
+    import matplotlib.pyplot as plt
+    have_matplotlib = True
+except:
+    have_matplotlib = False
+
+
+g1 = [1.006, 0.996, 0.998, 1.000, 0.992, 0.993, 1.002, 0.999, 0.994, 1.000]
+g2 = [0.998, 1.006, 1.000, 1.002, 0.997, 0.998, 0.996, 1.000, 1.006, 0.988]
+g3 = [0.991, 0.987, 0.997, 0.999, 0.995, 0.994, 1.000, 0.999, 0.996, 0.996]
+g4 = [1.005, 1.002, 0.994, 1.000, 0.995, 0.994, 0.998, 0.996, 1.002, 0.996]
+g5 = [0.998, 0.998, 0.982, 0.990, 1.002, 0.984, 0.996, 0.993, 0.980, 0.996]
+g6 = [1.009, 1.013, 1.009, 0.997, 0.988, 1.002, 0.995, 0.998, 0.981, 0.996]
+g7 = [0.990, 1.004, 0.996, 1.001, 0.998, 1.000, 1.018, 1.010, 0.996, 1.002]
+g8 = [0.998, 1.000, 1.006, 1.000, 1.002, 0.996, 0.998, 0.996, 1.002, 1.006]
+g9 = [1.002, 0.998, 0.996, 0.995, 0.996, 1.004, 1.004, 0.998, 0.999, 0.991]
+g10 = [0.991, 0.995, 0.984, 0.994, 0.997, 0.997, 0.991, 0.998, 1.004, 0.997]
+
+
+class TestShapiro(TestCase):
+    def test_basic(self):
+        x1 = [0.11,7.87,4.61,10.14,7.95,3.14,0.46,
+              4.43,0.21,4.75,0.71,1.52,3.24,
+              0.93,0.42,4.97,9.53,4.55,0.47,6.66]
+        w,pw = stats.shapiro(x1)
+        assert_almost_equal(w,0.90047299861907959,6)
+        assert_almost_equal(pw,0.042089745402336121,6)
+        x2 = [1.36,1.14,2.92,2.55,1.46,1.06,5.27,-1.11,
+              3.48,1.10,0.88,-0.51,1.46,0.52,6.20,1.69,
+              0.08,3.67,2.81,3.49]
+        w,pw = stats.shapiro(x2)
+        assert_almost_equal(w,0.9590270,6)
+        assert_almost_equal(pw,0.52460,3)
+
+    def test_bad_arg(self):
+        # Length of x is less than 3.
+        x = [1]
+        assert_raises(ValueError, stats.shapiro, x)
+
+
+class TestAnderson(TestCase):
+    def test_normal(self):
+        rs = RandomState(1234567890)
+        x1 = rs.standard_exponential(size=50)
+        x2 = rs.standard_normal(size=50)
+        A,crit,sig = stats.anderson(x1)
+        assert_array_less(crit[:-1], A)
+        A,crit,sig = stats.anderson(x2)
+        assert_array_less(A, crit[-2:])
+
+    def test_expon(self):
+        rs = RandomState(1234567890)
+        x1 = rs.standard_exponential(size=50)
+        x2 = rs.standard_normal(size=50)
+        A,crit,sig = stats.anderson(x1,'expon')
+        assert_array_less(A, crit[-2:])
+        olderr = np.seterr(all='ignore')
+        try:
+            A,crit,sig = stats.anderson(x2,'expon')
+        finally:
+            np.seterr(**olderr)
+        assert_(A > crit[-1])
+
+    def test_bad_arg(self):
+        assert_raises(ValueError, stats.anderson, [1], dist='plate_of_shrimp')
+
+
+class TestAnsari(TestCase):
+
+    def test_small(self):
+        x = [1,2,3,3,4]
+        y = [3,2,6,1,6,1,4,1]
+        W, pval = stats.ansari(x,y)
+        assert_almost_equal(W,23.5,11)
+        assert_almost_equal(pval,0.13499256881897437,11)
+
+    def test_approx(self):
+        ramsay = np.array((111, 107, 100, 99, 102, 106, 109, 108, 104, 99,
+                           101, 96, 97, 102, 107, 113, 116, 113, 110, 98))
+        parekh = np.array((107, 108, 106, 98, 105, 103, 110, 105, 104,
+                           100, 96, 108, 103, 104, 114, 114, 113, 108, 106, 99))
+
+        with warnings.catch_warnings():
+            warnings.filterwarnings('ignore',
+                        message="Ties preclude use of exact statistic.")
+            W, pval = stats.ansari(ramsay, parekh)
+
+        assert_almost_equal(W,185.5,11)
+        assert_almost_equal(pval,0.18145819972867083,11)
+
+    def test_exact(self):
+        W,pval = stats.ansari([1,2,3,4],[15,5,20,8,10,12])
+        assert_almost_equal(W,10.0,11)
+        assert_almost_equal(pval,0.533333333333333333,7)
+
+    def test_bad_arg(self):
+        assert_raises(ValueError, stats.ansari, [], [1])
+        assert_raises(ValueError, stats.ansari, [1], [])
+
+
+class TestBartlett(TestCase):
+
+    def test_data(self):
+        args = [g1, g2, g3, g4, g5, g6, g7, g8, g9, g10]
+        T, pval = stats.bartlett(*args)
+        assert_almost_equal(T,20.78587342806484,7)
+        assert_almost_equal(pval,0.0136358632781,7)
+
+    def test_bad_arg(self):
+        # Too few args raises ValueError.
+        assert_raises(ValueError, stats.bartlett, [1])
+
+
+class TestLevene(TestCase):
+
+    def test_data(self):
+        args = [g1, g2, g3, g4, g5, g6, g7, g8, g9, g10]
+        W, pval = stats.levene(*args)
+        assert_almost_equal(W,1.7059176930008939,7)
+        assert_almost_equal(pval,0.0990829755522,7)
+
+    def test_trimmed1(self):
+        # Test that center='trimmed' gives the same result as center='mean'
+        # when proportiontocut=0.
+        W1, pval1 = stats.levene(g1, g2, g3, center='mean')
+        W2, pval2 = stats.levene(g1, g2, g3, center='trimmed', proportiontocut=0.0)
+        assert_almost_equal(W1, W2)
+        assert_almost_equal(pval1, pval2)
+
+    def test_trimmed2(self):
+        x = [1.2, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 100.0]
+        y = [0.0, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 200.0]
+        np.random.seed(1234)
+        x2 = np.random.permutation(x)
+
+        # Use center='trimmed'
+        W0, pval0 = stats.levene(x, y, center='trimmed', proportiontocut=0.125)
+        W1, pval1 = stats.levene(x2, y, center='trimmed', proportiontocut=0.125)
+        # Trim the data here, and use center='mean'
+        W2, pval2 = stats.levene(x[1:-1], y[1:-1], center='mean')
+        # Result should be the same.
+        assert_almost_equal(W0, W2)
+        assert_almost_equal(W1, W2)
+        assert_almost_equal(pval1, pval2)
+
+    def test_equal_mean_median(self):
+        x = np.linspace(-1,1,21)
+        np.random.seed(1234)
+        x2 = np.random.permutation(x)
+        y = x**3
+        W1, pval1 = stats.levene(x, y, center='mean')
+        W2, pval2 = stats.levene(x2, y, center='median')
+        assert_almost_equal(W1, W2)
+        assert_almost_equal(pval1, pval2)
+
+    def test_bad_keyword(self):
+        x = np.linspace(-1,1,21)
+        assert_raises(TypeError, stats.levene, x, x, portiontocut=0.1)
+
+    def test_bad_center_value(self):
+        x = np.linspace(-1,1,21)
+        assert_raises(ValueError, stats.levene, x, x, center='trim')
+
+    def test_too_few_args(self):
+        assert_raises(ValueError, stats.levene, [1])
+
+
+class TestBinomP(TestCase):
+
+    def test_data(self):
+        pval = stats.binom_test(100,250)
+        assert_almost_equal(pval,0.0018833009350757682,11)
+        pval = stats.binom_test(201,405)
+        assert_almost_equal(pval,0.92085205962670713,11)
+        pval = stats.binom_test([682,243],p=3.0/4)
+        assert_almost_equal(pval,0.38249155957481695,11)
+
+    def test_bad_len_x(self):
+        # Length of x must be 1 or 2.
+        assert_raises(ValueError, stats.binom_test, [1,2,3])
+
+    def test_bad_n(self):
+        # len(x) is 1, but n is invalid.
+        # Missing n
+        assert_raises(ValueError, stats.binom_test, [100])
+        # n less than x[0]
+        assert_raises(ValueError, stats.binom_test, [100], n=50)
+
+    def test_bad_p(self):
+        assert_raises(ValueError, stats.binom_test, [50, 50], p=2.0)
+
+
+class TestFindRepeats(TestCase):
+
+    def test_basic(self):
+        a = [1,2,3,4,1,2,3,4,1,2,5]
+        res,nums = stats.find_repeats(a)
+        assert_array_equal(res,[1,2,3,4])
+        assert_array_equal(nums,[3,3,2,2])
+
+    def test_empty_result(self):
+        # Check that empty arrays are returned when there are no repeats.
+        a = [10, 20, 50, 30, 40]
+        repeated, counts = stats.find_repeats(a)
+        assert_array_equal(repeated, [])
+        assert_array_equal(counts, [])
+
+
+class TestFligner(TestCase):
+
+    def test_data(self):
+        # numbers from R: fligner.test in package stats
+        x1 = np.arange(5)
+        assert_array_almost_equal(stats.fligner(x1,x1**2),
+                           (3.2282229927203536, 0.072379187848207877), 11)
+
+    def test_trimmed1(self):
+        # Test that center='trimmed' gives the same result as center='mean'
+        # when proportiontocut=0.
+        Xsq1, pval1 = stats.fligner(g1, g2, g3, center='mean')
+        Xsq2, pval2 = stats.fligner(g1, g2, g3, center='trimmed', proportiontocut=0.0)
+        assert_almost_equal(Xsq1, Xsq2)
+        assert_almost_equal(pval1, pval2)
+
+    def test_trimmed2(self):
+        x = [1.2, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 100.0]
+        y = [0.0, 3.0, 3.5, 4.0, 4.5, 5.0, 5.5, 200.0]
+        # Use center='trimmed'
+        Xsq1, pval1 = stats.fligner(x, y, center='trimmed', proportiontocut=0.125)
+        # Trim the data here, and use center='mean'
+        Xsq2, pval2 = stats.fligner(x[1:-1], y[1:-1], center='mean')
+        # Result should be the same.
+        assert_almost_equal(Xsq1, Xsq2)
+        assert_almost_equal(pval1, pval2)
+
+    # The following test looks reasonable at first, but fligner() uses the
+    # function stats.rankdata(), and in one of the cases in this test,
+    # there are ties, while in the other (because of normal rounding
+    # errors) there are not.  This difference leads to differences in the
+    # third significant digit of W.
+    #
+    #def test_equal_mean_median(self):
+    #    x = np.linspace(-1,1,21)
+    #    y = x**3
+    #    W1, pval1 = stats.fligner(x, y, center='mean')
+    #    W2, pval2 = stats.fligner(x, y, center='median')
+    #    assert_almost_equal(W1, W2)
+    #    assert_almost_equal(pval1, pval2)
+
+    def test_bad_keyword(self):
+        x = np.linspace(-1,1,21)
+        assert_raises(TypeError, stats.fligner, x, x, portiontocut=0.1)
+
+    def test_bad_center_value(self):
+        x = np.linspace(-1,1,21)
+        assert_raises(ValueError, stats.fligner, x, x, center='trim')
+
+    def test_bad_num_args(self):
+        # Too few args raises ValueError.
+        assert_raises(ValueError, stats.fligner, [1])
+
+
+class TestMood(TestCase):
+    def test_mood(self):
+        # numbers from R: mood.test in package stats
+        x1 = np.arange(5)
+        assert_array_almost_equal(stats.mood(x1, x1**2),
+                                  (-1.3830857299399906, 0.16663858066771478), 11)
+
+    def test_mood_order_of_args(self):
+        # z should change sign when the order of arguments changes, pvalue
+        # should not change
+        np.random.seed(1234)
+        x1 = np.random.randn(10, 1)
+        x2 = np.random.randn(15, 1)
+        z1, p1 = stats.mood(x1, x2)
+        z2, p2 = stats.mood(x2, x1)
+        assert_array_almost_equal([z1, p1], [-z2, p2])
+
+    def test_mood_with_axis_none(self):
+        #Test with axis = None, compare with results from R
+        x1 = [-0.626453810742332, 0.183643324222082, -0.835628612410047,
+               1.59528080213779, 0.329507771815361, -0.820468384118015,
+               0.487429052428485, 0.738324705129217, 0.575781351653492,
+              -0.305388387156356, 1.51178116845085, 0.389843236411431,
+              -0.621240580541804, -2.2146998871775, 1.12493091814311,
+              -0.0449336090152309, -0.0161902630989461, 0.943836210685299,
+               0.821221195098089, 0.593901321217509]
+
+        x2 = [-0.896914546624981, 0.184849184646742, 1.58784533120882,
+              -1.13037567424629, -0.0802517565509893, 0.132420284381094,
+               0.707954729271733, -0.23969802417184, 1.98447393665293,
+              -0.138787012119665, 0.417650750792556, 0.981752777463662,
+              -0.392695355503813, -1.03966897694891, 1.78222896030858,
+              -2.31106908460517, 0.878604580921265, 0.035806718015226,
+               1.01282869212708, 0.432265154539617, 2.09081920524915,
+              -1.19992581964387, 1.58963820029007, 1.95465164222325,
+               0.00493777682814261, -2.45170638784613, 0.477237302613617,
+              -0.596558168631403, 0.792203270299649, 0.289636710177348]
+
+        x1 = np.array(x1)
+        x2 = np.array(x2)
+        x1.shape = (10, 2)
+        x2.shape = (15, 2)
+        assert_array_almost_equal(stats.mood(x1, x2, axis=None),
+                                  [-1.31716607555, 0.18778296257])
+
+    def test_mood_2d(self):
+        # Test if the results of mood test in 2-D case are consistent with the
+        # R result for the same inputs.  Numbers from R mood.test().
+        ny = 5
+        np.random.seed(1234)
+        x1 = np.random.randn(10, ny)
+        x2 = np.random.randn(15, ny)
+        z_vectest, pval_vectest = stats.mood(x1, x2)
+
+        for j in range(ny):
+            assert_array_almost_equal([z_vectest[j], pval_vectest[j]],
+                                      stats.mood(x1[:, j], x2[:, j]))
+
+        # inverse order of dimensions
+        x1 = x1.transpose()
+        x2 = x2.transpose()
+        z_vectest, pval_vectest = stats.mood(x1, x2, axis=1)
+
+        for i in range(ny):
+            # check axis handling is self consistent
+            assert_array_almost_equal([z_vectest[i], pval_vectest[i]],
+                                      stats.mood(x1[i, :], x2[i, :]))
+
+    def test_mood_3d(self):
+        shape = (10, 5, 6)
+        np.random.seed(1234)
+        x1 = np.random.randn(*shape)
+        x2 = np.random.randn(*shape)
+
+        for axis in range(3):
+            z_vectest, pval_vectest = stats.mood(x1, x2, axis=axis)
+            # Tests that result for 3-D arrays is equal to that for the
+            # same calculation on a set of 1-D arrays taken from the
+            # 3-D array
+            axes_idx = ([1, 2], [0, 2], [0, 1])  # the two axes != axis
+            for i in range(shape[axes_idx[axis][0]]):
+                for j in range(shape[axes_idx[axis][1]]):
+                    if axis == 0:
+                        slice1 = x1[:, i, j]
+                        slice2 = x2[:, i, j]
+                    elif axis == 1:
+                        slice1 = x1[i, :, j]
+                        slice2 = x2[i, :, j]
+                    else:
+                        slice1 = x1[i, j, :]
+                        slice2 = x2[i, j, :]
+
+                    assert_array_almost_equal([z_vectest[i, j],
+                                               pval_vectest[i, j]],
+                                              stats.mood(slice1, slice2))
+
+    def test_mood_bad_arg(self):
+        # Raise ValueError when the sum of the lengths of the args is less than 3
+        assert_raises(ValueError, stats.mood, [1], [])
+
+
+class TestProbplot(TestCase):
+
+    def test_basic(self):
+        np.random.seed(12345)
+        x = stats.norm.rvs(size=20)
+        osm, osr = stats.probplot(x, fit=False)
+        osm_expected = [-1.8241636, -1.38768012, -1.11829229, -0.91222575,
+                        -0.73908135, -0.5857176, -0.44506467, -0.31273668,
+                        -0.18568928, -0.06158146, 0.06158146, 0.18568928,
+                        0.31273668, 0.44506467, 0.5857176, 0.73908135,
+                        0.91222575, 1.11829229, 1.38768012, 1.8241636]
+        assert_allclose(osr, np.sort(x))
+        assert_allclose(osm, osm_expected)
+
+        res, res_fit = stats.probplot(x, fit=True)
+        res_fit_expected = [1.05361841, 0.31297795, 0.98741609]
+        assert_allclose(res_fit, res_fit_expected)
+
+    def test_sparams_keyword(self):
+        np.random.seed(123456)
+        x = stats.norm.rvs(size=100)
+        # Check that None, () and 0 (loc=0, for normal distribution) all work
+        # and give the same results
+        osm1, osr1 = stats.probplot(x, sparams=None, fit=False)
+        osm2, osr2 = stats.probplot(x, sparams=0, fit=False)
+        osm3, osr3 = stats.probplot(x, sparams=(), fit=False)
+        assert_allclose(osm1, osm2)
+        assert_allclose(osm1, osm3)
+        assert_allclose(osr1, osr2)
+        assert_allclose(osr1, osr3)
+        # Check giving (loc, scale) params for normal distribution
+        osm, osr = stats.probplot(x, sparams=(), fit=False)
+
+    def test_dist_keyword(self):
+        np.random.seed(12345)
+        x = stats.norm.rvs(size=20)
+        osm1, osr1 = stats.probplot(x, fit=False, dist='t', sparams=(3,))
+        osm2, osr2 = stats.probplot(x, fit=False, dist=stats.t, sparams=(3,))
+        assert_allclose(osm1, osm2)
+        assert_allclose(osr1, osr2)
+
+        assert_raises(ValueError, stats.probplot, x, dist='wrong-dist-name')
+        assert_raises(AttributeError, stats.probplot, x, dist=[])
+
+        class custom_dist(object):
+            """Some class that looks just enough like a distribution."""
+            def ppf(self, q):
+                return stats.norm.ppf(q, loc=2)
+
+        osm1, osr1 = stats.probplot(x, sparams=(2,), fit=False)
+        osm2, osr2 = stats.probplot(x, dist=custom_dist(), fit=False)
+        assert_allclose(osm1, osm2)
+        assert_allclose(osr1, osr2)
+
+    @dec.skipif(not have_matplotlib)
+    def test_plot_kwarg(self):
+        np.random.seed(7654321)
+        fig = plt.figure()
+        fig.add_subplot(111)
+        x = stats.t.rvs(3, size=100)
+        res1, fitres1 = stats.probplot(x, plot=plt)
+        plt.close()
+        res2, fitres2 = stats.probplot(x, plot=None)
+        res3 = stats.probplot(x, fit=False, plot=plt)
+        plt.close()
+        res4 = stats.probplot(x, fit=False, plot=None)
+        # Check that results are consistent between combinations of `fit` and
+        # `plot` keywords.
+        assert_(len(res1) == len(res2) == len(res3) == len(res4) == 2)
+        assert_allclose(res1, res2)
+        assert_allclose(res1, res3)
+        assert_allclose(res1, res4)
+        assert_allclose(fitres1, fitres2)
+
+        # Check that a Matplotlib Axes object is accepted
+        fig = plt.figure()
+        ax = fig.add_subplot(111)
+        stats.probplot(x, fit=False, plot=ax)
+        plt.close()
+
+    def test_probplot_bad_args(self):
+        # Raise ValueError when given an invalid distribution.
+        assert_raises(ValueError, stats.probplot, [1], dist="plate_of_shrimp")
+
+
+def test_wilcoxon_bad_arg():
+    # Raise ValueError when two args of different lengths are given or
+    # zero_method is unknown.
+    assert_raises(ValueError, stats.wilcoxon, [1], [1,2])
+    assert_raises(ValueError, stats.wilcoxon, [1,2], [1,2], "dummy")
+
+
+def test_mvsdist_bad_arg():
+    # Raise ValueError if fewer than two data points are given.
+    data = [1]
+    assert_raises(ValueError, stats.mvsdist, data)
+
+
+def test_kstat_bad_arg():
+    # Raise ValueError if n > 4 or n > 1.
+    data = [1]
+    n = 10
+    assert_raises(ValueError, stats.kstat, data, n=n)
+
+
+def test_kstatvar_bad_arg():
+    # Raise ValueError is n is not 1 or 2.
+    data = [1]
+    n = 10
+    assert_raises(ValueError, stats.kstatvar, data, n=n)
+
+
+def test_ppcc_max_bad_arg():
+    # Raise ValueError when given an invalid distribution.
+    data = [1]
+    assert_raises(ValueError, stats.ppcc_max, data, dist="plate_of_shrimp")
+
+
+class TestBoxcox_llf(TestCase):
+
+    def test_basic(self):
+        np.random.seed(54321)
+        x = stats.norm.rvs(size=10000, loc=10)
+        lmbda = 1
+        llf = stats.boxcox_llf(lmbda, x)
+        llf_expected = -x.size / 2. * np.log(np.sum(x.std()**2))
+        assert_allclose(llf, llf_expected)
+
+    def test_array_like(self):
+        np.random.seed(54321)
+        x = stats.norm.rvs(size=100, loc=10)
+        lmbda = 1
+        llf = stats.boxcox_llf(lmbda, x)
+        llf2 = stats.boxcox_llf(lmbda, list(x))
+        assert_allclose(llf, llf2, rtol=1e-12)
+
+    def test_2d_input(self):
+        # Note: boxcox_llf() was already working with 2-D input (sort of), so
+        # keep it like that.  boxcox() doesn't work with 2-D input though, due
+        # to brent() returning a scalar.
+        np.random.seed(54321)
+        x = stats.norm.rvs(size=100, loc=10)
+        lmbda = 1
+        llf = stats.boxcox_llf(lmbda, x)
+        llf2 = stats.boxcox_llf(lmbda, np.vstack([x, x]).T)
+        assert_allclose([llf, llf], llf2, rtol=1e-12)
+
+    def test_empty(self):
+        assert_(np.isnan(stats.boxcox_llf(1, [])))
+
+
+class TestBoxcox(TestCase):
+
+    def test_fixed_lmbda(self):
+        np.random.seed(12345)
+        x = stats.loggamma.rvs(5, size=50) + 5
+        xt = stats.boxcox(x, lmbda=1)
+        assert_allclose(xt, x - 1)
+        xt = stats.boxcox(x, lmbda=-1)
+        assert_allclose(xt, 1 - 1/x)
+
+        xt = stats.boxcox(x, lmbda=0)
+        assert_allclose(xt, np.log(x))
+
+        # Also test that array_like input works
+        xt = stats.boxcox(list(x), lmbda=0)
+        assert_allclose(xt, np.log(x))
+
+    def test_lmbda_None(self):
+        np.random.seed(1234567)
+        # Start from normal rv's, do inverse transform to check that
+        # optimization function gets close to the right answer.
+        np.random.seed(1245)
+        lmbda = 2.5
+        x = stats.norm.rvs(loc=10, size=50000)
+        x_inv = (x * lmbda + 1)**(-lmbda)
+        xt, maxlog = stats.boxcox(x_inv)
+
+        assert_almost_equal(maxlog, -1 / lmbda, decimal=2)
+
+    def test_alpha(self):
+        np.random.seed(1234)
+        x = stats.loggamma.rvs(5, size=50) + 5
+
+        # Some regular values for alpha, on a small sample size
+        _, _, interval = stats.boxcox(x, alpha=0.75)
+        assert_allclose(interval, [4.004485780226041, 5.138756355035744])
+        _, _, interval = stats.boxcox(x, alpha=0.05)
+        assert_allclose(interval, [1.2138178554857557, 8.209033272375663])
+
+        # Try some extreme values, see we don't hit the N=500 limit
+        x = stats.loggamma.rvs(7, size=500) + 15
+        _, _, interval = stats.boxcox(x, alpha=0.001)
+        assert_allclose(interval, [0.3988867, 11.40553131])
+        _, _, interval = stats.boxcox(x, alpha=0.999)
+        assert_allclose(interval, [5.83316246, 5.83735292])
+
+    def test_boxcox_bad_arg(self):
+        # Raise ValueError if any data value is negative.
+        x = np.array([-1])
+        assert_raises(ValueError, stats.boxcox, x)
+
+    def test_empty(self):
+        assert_(stats.boxcox([]).shape == (0,))
+
+
+class TestBoxcoxNormmax(TestCase):
+    def setUp(self):
+        np.random.seed(12345)
+        self.x = stats.loggamma.rvs(5, size=50) + 5
+
+    def test_pearsonr(self):
+        maxlog = stats.boxcox_normmax(self.x)
+        assert_allclose(maxlog, 1.804465325046)
+
+    def test_mle(self):
+        maxlog = stats.boxcox_normmax(self.x, method='mle')
+        assert_allclose(maxlog, 1.758101454114)
+
+        # Check that boxcox() uses 'mle'
+        _, maxlog_boxcox = stats.boxcox(self.x)
+        assert_allclose(maxlog_boxcox, maxlog)
+
+    def test_all(self):
+        maxlog_all = stats.boxcox_normmax(self.x, method='all')
+        assert_allclose(maxlog_all, [1.804465325046, 1.758101454114])
+
+
+class TestBoxcoxNormplot(TestCase):
+    def setUp(self):
+        np.random.seed(7654321)
+        self.x = stats.loggamma.rvs(5, size=500) + 5
+
+    def test_basic(self):
+        N = 5
+        lmbdas, ppcc = stats.boxcox_normplot(self.x, -10, 10, N=N)
+        ppcc_expected = [0.57783375, 0.83610988, 0.97524311, 0.99756057,
+                         0.95843297]
+        assert_allclose(lmbdas, np.linspace(-10, 10, num=N))
+        assert_allclose(ppcc, ppcc_expected)
+
+    @dec.skipif(not have_matplotlib)
+    def test_plot_kwarg(self):
+        # Check with the matplotlib.pyplot module
+        fig = plt.figure()
+        fig.add_subplot(111)
+        stats.boxcox_normplot(self.x, -20, 20, plot=plt)
+        plt.close()
+
+        # Check that a Matplotlib Axes object is accepted
+        fig.add_subplot(111)
+        ax = fig.add_subplot(111)
+        stats.boxcox_normplot(self.x, -20, 20, plot=ax)
+        plt.close()
+
+    def test_invalid_inputs(self):
+        # `lb` has to be larger than `la`
+        assert_raises(ValueError, stats.boxcox_normplot, self.x, 1, 0)
+        # `x` can not contain negative values
+        assert_raises(ValueError, stats.boxcox_normplot, [-1, 1] , 0, 1)
+
+    def test_empty(self):
+        assert_(stats.boxcox_normplot([], 0, 1).size == 0)
+
+
+class TestCircFuncs(TestCase):
+    def test_circfuncs(self):
+        x = np.array([355,5,2,359,10,350])
+        M = stats.circmean(x, high=360)
+        Mval = 0.167690146
+        assert_allclose(M, Mval, rtol=1e-7)
+
+        V = stats.circvar(x, high=360)
+        Vval = 42.51955609
+        assert_allclose(V, Vval, rtol=1e-7)
+
+        S = stats.circstd(x, high=360)
+        Sval = 6.520702116
+        assert_allclose(S, Sval, rtol=1e-7)
+
+    def test_circfuncs_small(self):
+        x = np.array([20,21,22,18,19,20.5,19.2])
+        M1 = x.mean()
+        M2 = stats.circmean(x, high=360)
+        assert_allclose(M2, M1, rtol=1e-5)
+
+        V1 = x.var()
+        V2 = stats.circvar(x, high=360)
+        assert_allclose(V2, V1, rtol=1e-4)
+
+        S1 = x.std()
+        S2 = stats.circstd(x, high=360)
+        assert_allclose(S2, S1, rtol=1e-4)
+
+    def test_circmean_axis(self):
+        x = np.array([[355,5,2,359,10,350],
+                      [351,7,4,352,9,349],
+                      [357,9,8,358,4,356]])
+        M1 = stats.circmean(x, high=360)
+        M2 = stats.circmean(x.ravel(), high=360)
+        assert_allclose(M1, M2, rtol=1e-14)
+
+        M1 = stats.circmean(x, high=360, axis=1)
+        M2 = [stats.circmean(x[i], high=360) for i in range(x.shape[0])]
+        assert_allclose(M1, M2, rtol=1e-14)
+
+        M1 = stats.circmean(x, high=360, axis=0)
+        M2 = [stats.circmean(x[:,i], high=360) for i in range(x.shape[1])]
+        assert_allclose(M1, M2, rtol=1e-14)
+
+    def test_circvar_axis(self):
+        x = np.array([[355,5,2,359,10,350],
+                      [351,7,4,352,9,349],
+                  [357,9,8,358,4,356]])
+
+        V1 = stats.circvar(x, high=360)
+        V2 = stats.circvar(x.ravel(), high=360)
+        assert_allclose(V1, V2, rtol=1e-11)
+
+        V1 = stats.circvar(x, high=360, axis=1)
+        V2 = [stats.circvar(x[i], high=360) for i in range(x.shape[0])]
+        assert_allclose(V1, V2, rtol=1e-11)
+
+        V1 = stats.circvar(x, high=360, axis=0)
+        V2 = [stats.circvar(x[:,i], high=360) for i in range(x.shape[1])]
+        assert_allclose(V1, V2, rtol=1e-11)
+
+    def test_circstd_axis(self):
+        x = np.array([[355,5,2,359,10,350],
+                      [351,7,4,352,9,349],
+                      [357,9,8,358,4,356]])
+
+        S1 = stats.circstd(x, high=360)
+        S2 = stats.circstd(x.ravel(), high=360)
+        assert_allclose(S1, S2, rtol=1e-11)
+
+        S1 = stats.circstd(x, high=360, axis=1)
+        S2 = [stats.circstd(x[i], high=360) for i in range(x.shape[0])]
+        assert_allclose(S1, S2, rtol=1e-11)
+
+        S1 = stats.circstd(x, high=360, axis=0)
+        S2 = [stats.circstd(x[:,i], high=360) for i in range(x.shape[1])]
+        assert_allclose(S1, S2, rtol=1e-11)
+
+    def test_circfuncs_array_like(self):
+        x = [355,5,2,359,10,350]
+        assert_allclose(stats.circmean(x, high=360), 0.167690146, rtol=1e-7)
+        assert_allclose(stats.circvar(x, high=360), 42.51955609, rtol=1e-7)
+        assert_allclose(stats.circstd(x, high=360), 6.520702116, rtol=1e-7)
+
+    def test_empty(self):
+        assert_(np.isnan(stats.circmean([])))
+        assert_(np.isnan(stats.circstd([])))
+        assert_(np.isnan(stats.circvar([])))
+
+
+def test_accuracy_wilcoxon():
+    freq = [1, 4, 16, 15, 8, 4, 5, 1, 2]
+    nums = range(-4, 5)
+    x = np.concatenate([[u] * v for u, v in zip(nums, freq)])
+    y = np.zeros(x.size)
+
+    T, p = stats.wilcoxon(x, y, "pratt")
+    assert_allclose(T, 423)
+    assert_allclose(p, 0.00197547303533107)
+
+    T, p = stats.wilcoxon(x, y, "zsplit")
+    assert_allclose(T, 441)
+    assert_allclose(p, 0.0032145343172473055)
+
+    T, p = stats.wilcoxon(x, y, "wilcox")
+    assert_allclose(T, 327)
+    assert_allclose(p, 0.00641346115861)
+
+    # Test the 'correction' option, using values computed in R with:
+    # > wilcox.test(x, y, paired=TRUE, exact=FALSE, correct={FALSE,TRUE})
+    x = np.array([120, 114, 181, 188, 180, 146, 121, 191, 132, 113, 127, 112])
+    y = np.array([133, 143, 119, 189, 112, 199, 198, 113, 115, 121, 142, 187])
+    T, p = stats.wilcoxon(x, y, correction=False)
+    assert_equal(T, 34)
+    assert_allclose(p, 0.6948866, rtol=1e-6)
+    T, p = stats.wilcoxon(x, y, correction=True)
+    assert_equal(T, 34)
+    assert_allclose(p, 0.7240817, rtol=1e-6)
+
+
+def test_wilcoxon_tie():
+    # Regression test for gh-2391.
+    # Corresponding R code is:
+    #   > result = wilcox.test(rep(0.1, 10), exact=FALSE, correct=FALSE)
+    #   > result$p.value
+    #   [1] 0.001565402
+    #   > result = wilcox.test(rep(0.1, 10), exact=FALSE, correct=TRUE)
+    #   > result$p.value
+    #   [1] 0.001904195
+    stat, p = stats.wilcoxon([0.1] * 10)
+    expected_p = 0.001565402
+    assert_equal(stat, 0)
+    assert_allclose(p, expected_p, rtol=1e-6)
+
+    stat, p = stats.wilcoxon([0.1] * 10, correction=True)
+    expected_p = 0.001904195
+    assert_equal(stat, 0)
+    assert_allclose(p, expected_p, rtol=1e-6)
+
+
+if __name__ == "__main__":
+    run_module_suite()

pywafo/src/wafo/stats/tests/test_mstats_extras.py

@@ -1,103 +1,107 @@
-# pylint: disable-msg=W0611, W0612, W0511,R0201
+# pylint: disable-msg=W0611, W0612, W0511,R0201
-"""Tests suite for maskedArray statistics.
+"""Tests suite for maskedArray statistics.
-
+
-:author: Pierre Gerard-Marchant
+:author: Pierre Gerard-Marchant
-:contact: pierregm_at_uga_dot_edu
+:contact: pierregm_at_uga_dot_edu
-"""
+"""
-__author__ = "Pierre GF Gerard-Marchant ($Author: backtopop $)"
+from __future__ import division, print_function, absolute_import
-
+
-import numpy as np
+__author__ = "Pierre GF Gerard-Marchant ($Author: backtopop $)"
-
+
-import numpy.ma as ma
+import numpy as np
-
+
-import scipy.stats.mstats as ms
+import numpy.ma as ma
-#import scipy.stats.mmorestats as mms
+
-
+import wafo.stats.mstats as ms
-from numpy.testing import TestCase, run_module_suite, assert_equal, \
+#import wafo.stats.mmorestats as mms
-    assert_almost_equal, assert_
+
-
+from numpy.testing import TestCase, run_module_suite, assert_equal, \
-
+    assert_almost_equal, assert_
-class TestMisc(TestCase):
+
-    #
+
-    def __init__(self, *args, **kwargs):
+class TestMisc(TestCase):
-        TestCase.__init__(self, *args, **kwargs)
+
-    #
+    def __init__(self, *args, **kwargs):
-    def test_mjci(self):
+        TestCase.__init__(self, *args, **kwargs)
-        "Tests the Marits-Jarrett estimator"
+
-        data = ma.array([ 77, 87, 88,114,151,210,219,246,253,262,
+    def test_mjci(self):
-                          296,299,306,376,428,515,666,1310,2611])
+        "Tests the Marits-Jarrett estimator"
-        assert_almost_equal(ms.mjci(data),[55.76819,45.84028,198.87875],5)
+        data = ma.array([77, 87, 88,114,151,210,219,246,253,262,
-    #
+                          296,299,306,376,428,515,666,1310,2611])
-    def test_trimmedmeanci(self):
+        assert_almost_equal(ms.mjci(data),[55.76819,45.84028,198.87875],5)
-        "Tests the confidence intervals of the trimmed mean."
+
-        data = ma.array([545,555,558,572,575,576,578,580,
+    def test_trimmedmeanci(self):
-                         594,605,635,651,653,661,666])
+        "Tests the confidence intervals of the trimmed mean."
-        assert_almost_equal(ms.trimmed_mean(data,0.2), 596.2, 1)
+        data = ma.array([545,555,558,572,575,576,578,580,
-        assert_equal(np.round(ms.trimmed_mean_ci(data,(0.2,0.2)),1),
+                         594,605,635,651,653,661,666])
-                     [561.8, 630.6])
+        assert_almost_equal(ms.trimmed_mean(data,0.2), 596.2, 1)
-    #
+        assert_equal(np.round(ms.trimmed_mean_ci(data,(0.2,0.2)),1),
-    def test_idealfourths(self):
+                     [561.8, 630.6])
-        "Tests ideal-fourths"
+
-        test = np.arange(100)
+    def test_idealfourths(self):
-        assert_almost_equal(np.asarray(ms.idealfourths(test)),
+        "Tests ideal-fourths"
-                            [24.416667,74.583333],6)
+        test = np.arange(100)
-        test_2D = test.repeat(3).reshape(-1,3)
+        assert_almost_equal(np.asarray(ms.idealfourths(test)),
-        assert_almost_equal(ms.idealfourths(test_2D, axis=0),
+                            [24.416667,74.583333],6)
-                            [[24.416667,24.416667,24.416667],
+        test_2D = test.repeat(3).reshape(-1,3)
-                             [74.583333,74.583333,74.583333]],6)
+        assert_almost_equal(ms.idealfourths(test_2D, axis=0),
-        assert_almost_equal(ms.idealfourths(test_2D, axis=1),
+                            [[24.416667,24.416667,24.416667],
-                            test.repeat(2).reshape(-1,2))
+                             [74.583333,74.583333,74.583333]],6)
-        test = [0,0]
+        assert_almost_equal(ms.idealfourths(test_2D, axis=1),
-        _result = ms.idealfourths(test)
+                            test.repeat(2).reshape(-1,2))
-        assert_(np.isnan(_result).all())
+        test = [0,0]
-
+        _result = ms.idealfourths(test)
-#..............................................................................
+        assert_(np.isnan(_result).all())
-class TestQuantiles(TestCase):
+
-    #
+#..............................................................................
-    def __init__(self, *args, **kwargs):
+
-        TestCase.__init__(self, *args, **kwargs)
+
-    #
+class TestQuantiles(TestCase):
-    def test_hdquantiles(self):
+
-        data = [0.706560797,0.727229578,0.990399276,0.927065621,0.158953014,
+    def __init__(self, *args, **kwargs):
-            0.887764025,0.239407086,0.349638551,0.972791145,0.149789972,
+        TestCase.__init__(self, *args, **kwargs)
-            0.936947700,0.132359948,0.046041972,0.641675031,0.945530547,
+
-            0.224218684,0.771450991,0.820257774,0.336458052,0.589113496,
+    def test_hdquantiles(self):
-            0.509736129,0.696838829,0.491323573,0.622767425,0.775189248,
+        data = [0.706560797,0.727229578,0.990399276,0.927065621,0.158953014,
-            0.641461450,0.118455200,0.773029450,0.319280007,0.752229111,
+            0.887764025,0.239407086,0.349638551,0.972791145,0.149789972,
-            0.047841438,0.466295911,0.583850781,0.840581845,0.550086491,
+            0.936947700,0.132359948,0.046041972,0.641675031,0.945530547,
-            0.466470062,0.504765074,0.226855960,0.362641207,0.891620942,
+            0.224218684,0.771450991,0.820257774,0.336458052,0.589113496,
-            0.127898691,0.490094097,0.044882048,0.041441695,0.317976349,
+            0.509736129,0.696838829,0.491323573,0.622767425,0.775189248,
-            0.504135618,0.567353033,0.434617473,0.636243375,0.231803616,
+            0.641461450,0.118455200,0.773029450,0.319280007,0.752229111,
-            0.230154113,0.160011327,0.819464108,0.854706985,0.438809221,
+            0.047841438,0.466295911,0.583850781,0.840581845,0.550086491,
-            0.487427267,0.786907310,0.408367937,0.405534192,0.250444460,
+            0.466470062,0.504765074,0.226855960,0.362641207,0.891620942,
-            0.995309248,0.144389588,0.739947527,0.953543606,0.680051621,
+            0.127898691,0.490094097,0.044882048,0.041441695,0.317976349,
-            0.388382017,0.863530727,0.006514031,0.118007779,0.924024803,
+            0.504135618,0.567353033,0.434617473,0.636243375,0.231803616,
-            0.384236354,0.893687694,0.626534881,0.473051932,0.750134705,
+            0.230154113,0.160011327,0.819464108,0.854706985,0.438809221,
-            0.241843555,0.432947602,0.689538104,0.136934797,0.150206859,
+            0.487427267,0.786907310,0.408367937,0.405534192,0.250444460,
-            0.474335206,0.907775349,0.525869295,0.189184225,0.854284286,
+            0.995309248,0.144389588,0.739947527,0.953543606,0.680051621,
-            0.831089744,0.251637345,0.587038213,0.254475554,0.237781276,
+            0.388382017,0.863530727,0.006514031,0.118007779,0.924024803,
-            0.827928620,0.480283781,0.594514455,0.213641488,0.024194386,
+            0.384236354,0.893687694,0.626534881,0.473051932,0.750134705,
-            0.536668589,0.699497811,0.892804071,0.093835427,0.731107772]
+            0.241843555,0.432947602,0.689538104,0.136934797,0.150206859,
-        #
+            0.474335206,0.907775349,0.525869295,0.189184225,0.854284286,
-        assert_almost_equal(ms.hdquantiles(data,[0., 1.]),
+            0.831089744,0.251637345,0.587038213,0.254475554,0.237781276,
-                            [0.006514031, 0.995309248])
+            0.827928620,0.480283781,0.594514455,0.213641488,0.024194386,
-        hdq = ms.hdquantiles(data,[0.25, 0.5, 0.75])
+            0.536668589,0.699497811,0.892804071,0.093835427,0.731107772]
-        assert_almost_equal(hdq, [0.253210762, 0.512847491, 0.762232442,])
+        #
-        hdq = ms.hdquantiles_sd(data,[0.25, 0.5, 0.75])
+        assert_almost_equal(ms.hdquantiles(data,[0., 1.]),
-        assert_almost_equal(hdq, [0.03786954, 0.03805389, 0.03800152,], 4)
+                            [0.006514031, 0.995309248])
-        #
+        hdq = ms.hdquantiles(data,[0.25, 0.5, 0.75])
-        data = np.array(data).reshape(10,10)
+        assert_almost_equal(hdq, [0.253210762, 0.512847491, 0.762232442,])
-        hdq = ms.hdquantiles(data,[0.25,0.5,0.75],axis=0)
+        hdq = ms.hdquantiles_sd(data,[0.25, 0.5, 0.75])
-        assert_almost_equal(hdq[:,0], ms.hdquantiles(data[:,0],[0.25,0.5,0.75]))
+        assert_almost_equal(hdq, [0.03786954, 0.03805389, 0.03800152,], 4)
-        assert_almost_equal(hdq[:,-1], ms.hdquantiles(data[:,-1],[0.25,0.5,0.75]))
+        #
-        hdq = ms.hdquantiles(data,[0.25,0.5,0.75],axis=0,var=True)
+        data = np.array(data).reshape(10,10)
-        assert_almost_equal(hdq[...,0],
+        hdq = ms.hdquantiles(data,[0.25,0.5,0.75],axis=0)
-                            ms.hdquantiles(data[:,0],[0.25,0.5,0.75],var=True))
+        assert_almost_equal(hdq[:,0], ms.hdquantiles(data[:,0],[0.25,0.5,0.75]))
-        assert_almost_equal(hdq[...,-1],
+        assert_almost_equal(hdq[:,-1], ms.hdquantiles(data[:,-1],[0.25,0.5,0.75]))
-                            ms.hdquantiles(data[:,-1],[0.25,0.5,0.75], var=True))
+        hdq = ms.hdquantiles(data,[0.25,0.5,0.75],axis=0,var=True)
-
+        assert_almost_equal(hdq[...,0],
-
+                            ms.hdquantiles(data[:,0],[0.25,0.5,0.75],var=True))
-###############################################################################
+        assert_almost_equal(hdq[...,-1],
-
+                            ms.hdquantiles(data[:,-1],[0.25,0.5,0.75], var=True))
-if __name__ == "__main__":
+
-    run_module_suite()
+
+###############################################################################
+
+if __name__ == "__main__":
+    run_module_suite()

pywafo/src/wafo/stats/tests/test_multivariate.py

@@ -0,0 +1,275 @@
+"""
+Test functions for multivariate normal distributions.
+
+"""
+from __future__ import division, print_function, absolute_import
+
+from numpy.testing import (assert_almost_equal,
+        run_module_suite, assert_allclose, assert_equal, assert_raises)
+
+import numpy
+import numpy as np
+
+import scipy.linalg
+import scipy.stats._multivariate
+from scipy.stats import multivariate_normal
+from scipy.stats import norm
+
+from scipy.stats._multivariate import _psd_pinv_decomposed_log_pdet
+
+from scipy.integrate import romb
+
+
+def test_scalar_values():
+    np.random.seed(1234)
+
+    # When evaluated on scalar data, the pdf should return a scalar
+    x, mean, cov = 1.5, 1.7, 2.5
+    pdf = multivariate_normal.pdf(x, mean, cov)
+    assert_equal(pdf.ndim, 0)
+
+    # When evaluated on a single vector, the pdf should return a scalar
+    x = np.random.randn(5)
+    mean = np.random.randn(5)
+    cov = np.abs(np.random.randn(5))  # Diagonal values for cov. matrix
+    pdf = multivariate_normal.pdf(x, mean, cov)
+    assert_equal(pdf.ndim, 0)
+
+
+def test_logpdf():
+    # Check that the log of the pdf is in fact the logpdf
+    np.random.seed(1234)
+    x = np.random.randn(5)
+    mean = np.random.randn(5)
+    cov = np.abs(np.random.randn(5))
+    d1 = multivariate_normal.logpdf(x, mean, cov)
+    d2 = multivariate_normal.pdf(x, mean, cov)
+    assert_allclose(d1, np.log(d2))
+
+
+def test_large_pseudo_determinant():
+    # Check that large pseudo-determinants are handled appropriately.
+
+    # Construct a singular diagonal covariance matrix
+    # whose pseudo determinant overflows double precision.
+    large_total_log = 1000.0
+    npos = 100
+    nzero = 2
+    large_entry = np.exp(large_total_log / npos)
+    n = npos + nzero
+    cov = np.zeros((n, n), dtype=float)
+    np.fill_diagonal(cov, large_entry)
+    cov[-nzero:, -nzero:] = 0
+
+    # Check some determinants.
+    assert_equal(scipy.linalg.det(cov), 0)
+    assert_equal(scipy.linalg.det(cov[:npos, :npos]), np.inf)
+
+    # np.linalg.slogdet is only available in numpy 1.6+
+    # but scipy currently supports numpy 1.5.1.
+    #assert_allclose(np.linalg.slogdet(cov[:npos, :npos]), (1, large_total_log))
+
+    # Check the pseudo-determinant.
+    U, log_pdet = scipy.stats._multivariate._psd_pinv_decomposed_log_pdet(cov)
+    assert_allclose(log_pdet, large_total_log)
+
+
+def test_broadcasting():
+    np.random.seed(1234)
+    n = 4
+
+    # Construct a random covariance matrix.
+    data = np.random.randn(n, n)
+    cov = np.dot(data, data.T)
+    mean = np.random.randn(n)
+
+    # Construct an ndarray which can be interpreted as
+    # a 2x3 array whose elements are random data vectors.
+    X = np.random.randn(2, 3, n)
+
+    # Check that multiple data points can be evaluated at once.
+    for i in range(2):
+        for j in range(3):
+            actual = multivariate_normal.pdf(X[i, j], mean, cov)
+            desired = multivariate_normal.pdf(X, mean, cov)[i, j]
+            assert_allclose(actual, desired)
+
+
+def test_normal_1D():
+    # The probability density function for a 1D normal variable should
+    # agree with the standard normal distribution in scipy.stats.distributions
+    x = np.linspace(0, 2, 10)
+    mean, cov = 1.2, 0.9
+    scale = cov**0.5
+    d1 = norm.pdf(x, mean, scale)
+    d2 = multivariate_normal.pdf(x, mean, cov)
+    assert_allclose(d1, d2)
+
+
+def test_marginalization():
+    # Integrating out one of the variables of a 2D Gaussian should
+    # yield a 1D Gaussian
+    mean = np.array([2.5, 3.5])
+    cov = np.array([[.5, 0.2], [0.2, .6]])
+    n = 2**8 + 1  # Number of samples
+    delta = 6 / (n - 1)  # Grid spacing
+
+    v = np.linspace(0, 6, n)
+    xv, yv = np.meshgrid(v, v)
+    pos = np.empty((n, n, 2))
+    pos[:, :, 0] = xv
+    pos[:, :, 1] = yv
+    pdf = multivariate_normal.pdf(pos, mean, cov)
+
+    # Marginalize over x and y axis
+    margin_x = romb(pdf, delta, axis=0)
+    margin_y = romb(pdf, delta, axis=1)
+
+    # Compare with standard normal distribution
+    gauss_x = norm.pdf(v, loc=mean[0], scale=cov[0, 0]**0.5)
+    gauss_y = norm.pdf(v, loc=mean[1], scale=cov[1, 1]**0.5)
+    assert_allclose(margin_x, gauss_x, rtol=1e-2, atol=1e-2)
+    assert_allclose(margin_y, gauss_y, rtol=1e-2, atol=1e-2)
+
+
+def test_frozen():
+    # The frozen distribution should agree with the regular one
+    np.random.seed(1234)
+    x = np.random.randn(5)
+    mean = np.random.randn(5)
+    cov = np.abs(np.random.randn(5))
+    norm_frozen = multivariate_normal(mean, cov)
+    assert_allclose(norm_frozen.pdf(x), multivariate_normal.pdf(x, mean, cov))
+    assert_allclose(norm_frozen.logpdf(x),
+                    multivariate_normal.logpdf(x, mean, cov))
+
+
+def test_pseudodet_pinv():
+    # Make sure that pseudo-inverse and pseudo-det agree on cutoff
+
+    # Assemble random covariance matrix with large and small eigenvalues
+    np.random.seed(1234)
+    n = 7
+    x = np.random.randn(n, n)
+    cov = np.dot(x, x.T)
+    s, u = scipy.linalg.eigh(cov)
+    s = 0.5 * np.ones(n)
+    s[0] = 1.0
+    s[-1] = 1e-7
+    cov = np.dot(u, np.dot(np.diag(s), u.T))
+
+    # Set cond so that the lowest eigenvalue is below the cutoff
+    cond = 1e-5
+    U, log_pdet = _psd_pinv_decomposed_log_pdet(cov, cond)
+    pinv = np.dot(U, U.T)
+    _, log_pdet_pinv = _psd_pinv_decomposed_log_pdet(pinv, cond)
+
+    # Check that the log pseudo-determinant agrees with the sum
+    # of the logs of all but the smallest eigenvalue
+    assert_allclose(log_pdet, np.sum(np.log(s[:-1])))
+    # Check that the pseudo-determinant of the pseudo-inverse
+    # agrees with 1 / pseudo-determinant
+    assert_allclose(-log_pdet, log_pdet_pinv)
+
+
+def test_exception_nonsquare_cov():
+    cov = [[1, 2, 3], [4, 5, 6]]
+    assert_raises(ValueError, _psd_pinv_decomposed_log_pdet, cov)
+
+
+def test_exception_nonfinite_cov():
+    cov_nan = [[1, 0], [0, np.nan]]
+    assert_raises(ValueError, _psd_pinv_decomposed_log_pdet, cov_nan)
+    cov_inf = [[1, 0], [0, np.inf]]
+    assert_raises(ValueError, _psd_pinv_decomposed_log_pdet, cov_inf)
+
+
+def test_exception_non_psd_cov():
+    cov = [[1, 0], [0, -1]]
+    assert_raises(ValueError, _psd_pinv_decomposed_log_pdet, cov)
+
+
+def test_R_values():
+    # Compare the multivariate pdf with some values precomputed
+    # in R version 3.0.1 (2013-05-16) on Mac OS X 10.6.
+
+    # The values below were generated by the following R-script:
+    # > library(mnormt)
+    # > x <- seq(0, 2, length=5)
+    # > y <- 3*x - 2
+    # > z <- x + cos(y)
+    # > mu <- c(1, 3, 2)
+    # > Sigma <- matrix(c(1,2,0,2,5,0.5,0,0.5,3), 3, 3)
+    # > r_pdf <- dmnorm(cbind(x,y,z), mu, Sigma)
+    r_pdf = np.array([0.0002214706, 0.0013819953, 0.0049138692,
+                      0.0103803050, 0.0140250800])
+
+    x = np.linspace(0, 2, 5)
+    y = 3 * x - 2
+    z = x + np.cos(y)
+    r = np.array([x, y, z]).T
+
+    mean = np.array([1, 3, 2], 'd')
+    cov = np.array([[1, 2, 0], [2, 5, .5], [0, .5, 3]], 'd')
+
+    pdf = multivariate_normal.pdf(r, mean, cov)
+    assert_allclose(pdf, r_pdf, atol=1e-10)
+
+
+def test_rvs_shape():
+    # Check that rvs parses the mean and covariance correctly, and returns
+    # an array of the right shape
+    N = 300
+    d = 4
+    sample = multivariate_normal.rvs(mean=np.zeros(d), cov=1, size=N)
+    assert_equal(sample.shape, (N, d))
+
+    sample = multivariate_normal.rvs(mean=None,
+                                     cov=np.array([[2, .1], [.1, 1]]),
+                                     size=N)
+    assert_equal(sample.shape, (N, 2))
+
+    u = multivariate_normal(mean=0, cov=1)
+    sample = u.rvs(N)
+    assert_equal(sample.shape, (N, ))
+
+
+def test_large_sample():
+    # Generate large sample and compare sample mean and sample covariance
+    # with mean and covariance matrix.
+
+    np.random.seed(2846)
+
+    n = 3
+    mean = np.random.randn(n)
+    M = np.random.randn(n, n)
+    cov = np.dot(M, M.T)
+    size = 5000
+
+    sample = multivariate_normal.rvs(mean, cov, size)
+
+    assert_allclose(numpy.cov(sample.T), cov, rtol=1e-1)
+    assert_allclose(sample.mean(0), mean, rtol=1e-1)
+
+
+def test_entropy():
+    np.random.seed(2846)
+
+    n = 3
+    mean = np.random.randn(n)
+    M = np.random.randn(n, n)
+    cov = np.dot(M, M.T)
+
+    rv = multivariate_normal(mean, cov)
+
+    # Check that frozen distribution agrees with entropy function
+    assert_almost_equal(rv.entropy(), multivariate_normal.entropy(mean, cov))
+    # Compare entropy with manually computed expression involving
+    # the sum of the logs of the eigenvalues of the covariance matrix
+    eigs = np.linalg.eig(cov)[0]
+    desired = 1/2 * (n * (np.log(2*np.pi) + 1) + np.sum(np.log(eigs)))
+    assert_almost_equal(desired, rv.entropy())
+
+
+if __name__ == "__main__":
+    run_module_suite()

pywafo/src/wafo/stats/tests/test_rank.py

@@ -0,0 +1,193 @@
+from __future__ import division, print_function, absolute_import
+
+import numpy as np
+from numpy.testing import TestCase, run_module_suite, assert_equal, \
+    assert_array_equal
+
+from scipy.stats import rankdata, tiecorrect
+
+
+class TestTieCorrect(TestCase):
+
+    def test_empty(self):
+        """An empty array requires no correction, should return 1.0."""
+        ranks = np.array([], dtype=np.float64)
+        c = tiecorrect(ranks)
+        assert_equal(c, 1.0)
+
+    def test_one(self):
+        """A single element requires no correction, should return 1.0."""
+        ranks = np.array([1.0], dtype=np.float64)
+        c = tiecorrect(ranks)
+        assert_equal(c, 1.0)
+
+    def test_no_correction(self):
+        """Arrays with no ties require no correction."""
+        ranks = np.arange(2.0)
+        c = tiecorrect(ranks)
+        assert_equal(c, 1.0)
+        ranks = np.arange(3.0)
+        c = tiecorrect(ranks)
+        assert_equal(c, 1.0)
+
+    def test_basic(self):
+        """Check a few basic examples of the tie correction factor."""
+        # One tie of two elements
+        ranks = np.array([1.0, 2.5, 2.5])
+        c = tiecorrect(ranks)
+        T = 2.0
+        N = ranks.size
+        expected = 1.0 - (T**3 - T) / (N**3 - N)
+        assert_equal(c, expected)
+
+        # One tie of two elements (same as above, but tie is not at the end)
+        ranks = np.array([1.5, 1.5, 3.0])
+        c = tiecorrect(ranks)
+        T = 2.0
+        N = ranks.size
+        expected = 1.0 - (T**3 - T) / (N**3 - N)
+        assert_equal(c, expected)
+
+        # One tie of three elements
+        ranks = np.array([1.0, 3.0, 3.0, 3.0])
+        c = tiecorrect(ranks)
+        T = 3.0
+        N = ranks.size
+        expected = 1.0 - (T**3 - T) / (N**3 - N)
+        assert_equal(c, expected)
+
+        # Two ties, lengths 2 and 3.
+        ranks = np.array([1.5, 1.5, 4.0, 4.0, 4.0])
+        c = tiecorrect(ranks)
+        T1 = 2.0
+        T2 = 3.0
+        N = ranks.size
+        expected = 1.0 - ((T1**3 - T1) + (T2**3 - T2)) / (N**3 - N)
+        assert_equal(c, expected)
+
+
+class TestRankData(TestCase):
+
+    def test_empty(self):
+        """stats.rankdata([]) should return an empty array."""
+        a = np.array([], dtype=np.int)
+        r = rankdata(a)
+        assert_array_equal(r, np.array([], dtype=np.float64))
+        r = rankdata([])
+        assert_array_equal(r, np.array([], dtype=np.float64))
+
+    def test_one(self):
+        """Check stats.rankdata with an array of length 1."""
+        data = [100]
+        a = np.array(data, dtype=np.int)
+        r = rankdata(a)
+        assert_array_equal(r, np.array([1.0], dtype=np.float64))
+        r = rankdata(data)
+        assert_array_equal(r, np.array([1.0], dtype=np.float64))
+
+    def test_basic(self):
+        """Basic tests of stats.rankdata."""
+        data = [100, 10, 50]
+        expected = np.array([3.0, 1.0, 2.0], dtype=np.float64)
+        a = np.array(data, dtype=np.int)
+        r = rankdata(a)
+        assert_array_equal(r, expected)
+        r = rankdata(data)
+        assert_array_equal(r, expected)
+
+        data = [40, 10, 30, 10, 50]
+        expected = np.array([4.0, 1.5, 3.0, 1.5, 5.0], dtype=np.float64)
+        a = np.array(data, dtype=np.int)
+        r = rankdata(a)
+        assert_array_equal(r, expected)
+        r = rankdata(data)
+        assert_array_equal(r, expected)
+
+        data = [20, 20, 20, 10, 10, 10]
+        expected = np.array([5.0, 5.0, 5.0, 2.0, 2.0, 2.0], dtype=np.float64)
+        a = np.array(data, dtype=np.int)
+        r = rankdata(a)
+        assert_array_equal(r, expected)
+        r = rankdata(data)
+        assert_array_equal(r, expected)
+        # The docstring states explicitly that the argument is flattened.
+        a2d = a.reshape(2, 3)
+        r = rankdata(a2d)
+        assert_array_equal(r, expected)
+
+    def test_large_int(self):
+        data = np.array([2**60, 2**60+1], dtype=np.uint64)
+        r = rankdata(data)
+        assert_array_equal(r, [1.0, 2.0])
+
+        data = np.array([2**60, 2**60+1], dtype=np.int64)
+        r = rankdata(data)
+        assert_array_equal(r, [1.0, 2.0])
+
+        data = np.array([2**60, -2**60+1], dtype=np.int64)
+        r = rankdata(data)
+        assert_array_equal(r, [2.0, 1.0])
+
+    def test_big_tie(self):
+        for n in [10000, 100000, 1000000]:
+            data = np.ones(n, dtype=int)
+            r = rankdata(data)
+            expected_rank = 0.5 * (n + 1)
+            assert_array_equal(r, expected_rank * data,
+                               "test failed with n=%d" % n)
+
+
+_cases = (
+    # values, method, expected
+    ([], 'average', []),
+    ([], 'min', []),
+    ([], 'max', []),
+    ([], 'dense', []),
+    ([], 'ordinal', []),
+    #
+    ([100], 'average', [1.0]),
+    ([100], 'min', [1.0]),
+    ([100], 'max', [1.0]),
+    ([100], 'dense', [1.0]),
+    ([100], 'ordinal', [1.0]),
+    #
+    ([100, 100, 100], 'average', [2.0, 2.0, 2.0]),
+    ([100, 100, 100], 'min', [1.0, 1.0, 1.0]),
+    ([100, 100, 100], 'max', [3.0, 3.0, 3.0]),
+    ([100, 100, 100], 'dense', [1.0, 1.0, 1.0]),
+    ([100, 100, 100], 'ordinal', [1.0, 2.0, 3.0]),
+    #
+    ([100, 300, 200], 'average', [1.0, 3.0, 2.0]),
+    ([100, 300, 200], 'min', [1.0, 3.0, 2.0]),
+    ([100, 300, 200], 'max', [1.0, 3.0, 2.0]),
+    ([100, 300, 200], 'dense', [1.0, 3.0, 2.0]),
+    ([100, 300, 200], 'ordinal', [1.0, 3.0, 2.0]),
+    #
+    ([100, 200, 300, 200], 'average', [1.0, 2.5, 4.0, 2.5]),
+    ([100, 200, 300, 200], 'min', [1.0, 2.0, 4.0, 2.0]),
+    ([100, 200, 300, 200], 'max', [1.0, 3.0, 4.0, 3.0]),
+    ([100, 200, 300, 200], 'dense', [1.0, 2.0, 3.0, 2.0]),
+    ([100, 200, 300, 200], 'ordinal', [1.0, 2.0, 4.0, 3.0]),
+    #
+    ([100, 200, 300, 200, 100], 'average', [1.5, 3.5, 5.0, 3.5, 1.5]),
+    ([100, 200, 300, 200, 100], 'min', [1.0, 3.0, 5.0, 3.0, 1.0]),
+    ([100, 200, 300, 200, 100], 'max', [2.0, 4.0, 5.0, 4.0, 2.0]),
+    ([100, 200, 300, 200, 100], 'dense', [1.0, 2.0, 3.0, 2.0, 1.0]),
+    ([100, 200, 300, 200, 100], 'ordinal', [1.0, 3.0, 5.0, 4.0, 2.0]),
+    #
+    ([10] * 30, 'ordinal', np.arange(1.0, 31.0)),
+)
+
+
+def test_cases():
+
+    def check_case(values, method, expected):
+        r = rankdata(values, method=method)
+        assert_array_equal(r, expected)
+
+    for values, method, expected in _cases:
+        yield check_case, values, method, expected
+
+
+if __name__ == "__main__":
+    run_module_suite()

pywafo/src/wafo/stats/tests/test_tukeylambda_stats.py

@@ -0,0 +1,91 @@
+from __future__ import division, print_function, absolute_import
+
+import numpy as np
+from numpy.testing import assert_allclose, assert_equal, run_module_suite
+
+from scipy.stats._tukeylambda_stats import tukeylambda_variance, \
+                                            tukeylambda_kurtosis
+
+
+def test_tukeylambda_stats_known_exact():
+    """Compare results with some known exact formulas."""
+    # Some exact values of the Tukey Lambda variance and kurtosis:
+    # lambda   var      kurtosis
+    #   0     pi**2/3     6/5     (logistic distribution)
+    #  0.5    4 - pi    (5/3 - pi/2)/(pi/4 - 1)**2 - 3
+    #   1      1/3       -6/5     (uniform distribution on (-1,1))
+    #   2      1/12      -6/5     (uniform distribution on (-1/2, 1/2))
+
+    # lambda = 0
+    var = tukeylambda_variance(0)
+    assert_allclose(var, np.pi**2 / 3, atol=1e-12)
+    kurt = tukeylambda_kurtosis(0)
+    assert_allclose(kurt, 1.2, atol=1e-10)
+
+    # lambda = 0.5
+    var = tukeylambda_variance(0.5)
+    assert_allclose(var, 4 - np.pi, atol=1e-12)
+    kurt = tukeylambda_kurtosis(0.5)
+    desired = (5./3 - np.pi/2) / (np.pi/4 - 1)**2 - 3
+    assert_allclose(kurt, desired, atol=1e-10)
+
+    # lambda = 1
+    var = tukeylambda_variance(1)
+    assert_allclose(var, 1.0 / 3, atol=1e-12)
+    kurt = tukeylambda_kurtosis(1)
+    assert_allclose(kurt, -1.2, atol=1e-10)
+
+    # lambda = 2
+    var = tukeylambda_variance(2)
+    assert_allclose(var, 1.0 / 12, atol=1e-12)
+    kurt = tukeylambda_kurtosis(2)
+    assert_allclose(kurt, -1.2, atol=1e-10)
+
+
+def test_tukeylambda_stats_mpmath():
+    """Compare results with some values that were computed using mpmath."""
+    a10 = dict(atol=1e-10, rtol=0)
+    a12 = dict(atol=1e-12, rtol=0)
+    data = [
+        # lambda        variance              kurtosis
+        [-0.1, 4.78050217874253547, 3.78559520346454510],
+        [-0.0649, 4.16428023599895777, 2.52019675947435718],
+        [-0.05, 3.93672267890775277, 2.13129793057777277],
+        [-0.001, 3.30128380390964882, 1.21452460083542988],
+        [0.001, 3.27850775649572176, 1.18560634779287585],
+        [0.03125, 2.95927803254615800, 0.804487555161819980],
+        [0.05, 2.78281053405464501, 0.611604043886644327],
+        [0.0649, 2.65282386754100551, 0.476834119532774540],
+        [1.2, 0.242153920578588346, -1.23428047169049726],
+        [10.0, 0.00095237579757703597, 2.37810697355144933],
+        [20.0, 0.00012195121951131043, 7.37654321002709531],
+    ]
+
+    for lam, var_expected, kurt_expected in data:
+        var = tukeylambda_variance(lam)
+        assert_allclose(var, var_expected, **a12)
+        kurt = tukeylambda_kurtosis(lam)
+        assert_allclose(kurt, kurt_expected, **a10)
+
+    # Test with vector arguments (most of the other tests are for single
+    # values).
+    lam, var_expected, kurt_expected = zip(*data)
+    var = tukeylambda_variance(lam)
+    assert_allclose(var, var_expected, **a12)
+    kurt = tukeylambda_kurtosis(lam)
+    assert_allclose(kurt, kurt_expected, **a10)
+
+
+def test_tukeylambda_stats_invalid():
+    """Test values of lambda outside the domains of the functions."""
+    lam = [-1.0, -0.5]
+    var = tukeylambda_variance(lam)
+    assert_equal(var, np.array([np.nan, np.inf]))
+
+    lam = [-1.0, -0.25]
+    kurt = tukeylambda_kurtosis(lam)
+    assert_equal(kurt, np.array([np.nan, np.inf]))
+
+
+if __name__ == "__main__":
+    run_module_suite()

pywafo/src/wafo/stats/vonmises.py

@@ -0,0 +1,47 @@
+from __future__ import division, print_function, absolute_import
+
+import numpy as np
+import scipy.stats
+from scipy.special import i0
+
+
+def von_mises_cdf_series(k,x,p):
+    x = float(x)
+    s = np.sin(x)
+    c = np.cos(x)
+    sn = np.sin(p*x)
+    cn = np.cos(p*x)
+    R = 0
+    V = 0
+    for n in range(p-1,0,-1):
+        sn, cn = sn*c - cn*s, cn*c + sn*s
+        R = 1./(2*n/k + R)
+        V = R*(sn/n+V)
+
+    return 0.5+x/(2*np.pi) + V/np.pi
+
+
+def von_mises_cdf_normalapprox(k,x,C1):
+    b = np.sqrt(2/np.pi)*np.exp(k)/i0(k)
+    z = b*np.sin(x/2.)
+    return scipy.stats.norm.cdf(z)
+
+
+def von_mises_cdf(k,x):
+    ix = 2*np.pi*np.round(x/(2*np.pi))
+    x = x-ix
+    k = float(k)
+
+    # These values should give 12 decimal digits
+    CK = 50
+    a = [28., 0.5, 100., 5.0]
+    C1 = 50.1
+
+    if k < CK:
+        p = int(np.ceil(a[0]+a[1]*k-a[2]/(k+a[3])))
+
+        F = np.clip(von_mises_cdf_series(k,x,p),0,1)
+    else:
+        F = von_mises_cdf_normalapprox(k,x,C1)
+
+    return F+ix

pywafo/src/wafo/stats/vonmises_cython.pyx

@@ -0,0 +1,76 @@
+import numpy as np
+import scipy.stats
+from scipy.special import i0
+import numpy.testing
+cimport numpy as np
+
+cdef extern from "math.h":
+    double cos(double theta)
+    double sin(double theta)
+
+
+cdef double von_mises_cdf_series(double k,double x,unsigned int p):
+    cdef double s, c, sn, cn, R, V
+    cdef unsigned int n
+    s = sin(x)
+    c = cos(x)
+    sn = sin(p*x)
+    cn = cos(p*x)
+    R = 0
+    V = 0
+    for n in range(p-1,0,-1):
+        sn, cn = sn*c - cn*s, cn*c + sn*s
+        R = 1./(2*n/k + R)
+        V = R*(sn/n+V)
+
+    return 0.5+x/(2*np.pi) + V/np.pi
+
+def von_mises_cdf_normalapprox(k,x,C1):
+    b = np.sqrt(2/np.pi)*np.exp(k)/i0(k)
+    z = b*np.sin(x/2.)
+    C = 24*k
+    chi = z - z**3/((C-2*z**2-16)/3.-(z**4+7/4.*z**2+167./2)/(C+C1-z**2+3))**2
+    return scipy.stats.norm.cdf(z)
+
+cimport cython
+@cython.boundscheck(False)
+def von_mises_cdf(k,x):
+    cdef np.ndarray[double, ndim=1] temp, temp_xs, temp_ks
+    cdef unsigned int i, p
+    cdef double a1, a2, a3, a4, C1, CK
+    #k,x = np.broadcast_arrays(np.asarray(k),np.asarray(x))
+    k = np.asarray(k)
+    x = np.asarray(x)
+    zerodim = k.ndim==0 and x.ndim==0
+
+    k = np.atleast_1d(k)
+    x = np.atleast_1d(x)
+    ix = np.round(x/(2*np.pi))
+    x = x-ix*2*np.pi
+
+    # These values should give 12 decimal digits
+    CK=50
+    a1, a2, a3, a4 = [28., 0.5, 100., 5.0]
+    C1 = 50.1
+
+    bx, bk = np.broadcast_arrays(x,k)
+    result = np.empty(bx.shape,dtype=np.float)
+     
+    c_small_k = bk<CK
+    temp = result[c_small_k]
+    temp_xs = bx[c_small_k].astype(np.float)
+    temp_ks = bk[c_small_k].astype(np.float)
+    for i in range(len(temp)):
+        p = <int>(1+a1+a2*temp_ks[i]-a3/(temp_ks[i]+a4))
+        temp[i] = von_mises_cdf_series(temp_ks[i],temp_xs[i],p)
+        if temp[i]<0:
+            temp[i]=0
+        elif temp[i]>1:
+            temp[i]=1
+    result[c_small_k] = temp
+    result[~c_small_k] = von_mises_cdf_normalapprox(bk[~c_small_k],bx[~c_small_k],C1)
+
+    if not zerodim:
+        return result+ix
+    else:
+        return (result+ix)[0]