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Upated wafo.stats

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master
Per A Brodtkorb 9 years ago
parent 939f2c7252
commit aeed49139b
1 changed files with 105 additions and 38 deletions
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141
wafo/stats/_continuous_distns.py
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@ -13,7 +13,8 @@ from scipy import optimize
from scipy import integrate
from scipy.special import (gammaln as gamln, gamma as gam, boxcox, boxcox1p,
inv_boxcox, inv_boxcox1p, erfc, chndtr, chndtrix,
log1p, expm1)
log1p, expm1,
i0, i1, ndtr as _norm_cdf, log_ndtr as _norm_logcdf)
from numpy import (where, arange, putmask, ravel, shape,
log, sqrt, exp, arctanh, tan, sin, arcsin, arctan,
@ -32,9 +33,8 @@ from scipy.stats._tukeylambda_stats import (tukeylambda_variance as _tlvar,
tukeylambda_kurtosis as _tlkurt)
from ._distn_infrastructure import (
rv_continuous, valarray, _skew, _kurtosis, # @UnresolvedImport
_lazywhere, _ncx2_log_pdf, _ncx2_pdf, _ncx2_cdf, # @UnresolvedImport
get_distribution_names, # @UnresolvedImport
rv_continuous, valarray, _skew, _kurtosis, _lazywhere,
_ncx2_log_pdf, _ncx2_pdf, _ncx2_cdf, get_distribution_names,
)
from ._constants import _XMIN, _EULER, _ZETA3, _XMAX, _LOGXMAX, _EPS
@ -89,24 +89,16 @@ def _norm_logpdf(x):
return -x**2 / 2.0 - _norm_pdf_logC
def _norm_cdf(x):
return special.ndtr(x)
def _norm_logcdf(x):
return special.log_ndtr(x)
def _norm_ppf(q):
return special.ndtri(q)
def _norm_sf(x):
return special.ndtr(-x)
return _norm_cdf(-x)
def _norm_logsf(x):
return special.log_ndtr(-x)
return _norm_logcdf(-x)
def _norm_isf(q):
@ -127,6 +119,10 @@ class norm_gen(rv_continuous):
norm.pdf(x) = exp(-x**2/2)/sqrt(2*pi)
The survival function, ``norm.sf``, is also referred to as the
Q-function in some contexts (see, e.g.,
`Wikipedia's <https://en.wikipedia.org/wiki/Q-function>`_ definition).
%(after_notes)s
%(example)s
@ -220,13 +216,13 @@ class alpha_gen(rv_continuous):
"""
def _pdf(self, x, a):
return 1.0/(x**2)/special.ndtr(a)*_norm_pdf(a-1.0/x)
return 1.0/(x**2)/_norm_cdf(a)*_norm_pdf(a-1.0/x)
def _logpdf(self, x, a):
return -2*log(x) + _norm_logpdf(a-1.0/x) - log(special.ndtr(a))
return -2*log(x) + _norm_logpdf(a-1.0/x) - log(_norm_cdf(a))
def _cdf(self, x, a):
return special.ndtr(a-1.0/x) / special.ndtr(a)
return _norm_cdf(a-1.0/x) / _norm_cdf(a)
def _ppf(self, q, a):
return 1.0/asarray(a-special.ndtri(q*special.ndtr(a)))
@ -1221,12 +1217,12 @@ class exponnorm_gen(rv_continuous):
def _cdf(self, x, K):
invK = 1.0 / K
expval = invK * (0.5 * invK - x)
return special.ndtr(x) - exp(expval) * special.ndtr(x - invK)
return _norm_cdf(x) - exp(expval) * _norm_cdf(x - invK)
def _sf(self, x, K):
invK = 1.0 / K
expval = invK * (0.5 * invK - x)
return special.ndtr(-x) + exp(expval) * special.ndtr(x - invK)
return _norm_cdf(-x) + exp(expval) * _norm_cdf(x - invK)
def _stats(self, K):
K2 = K * K
@ -1366,7 +1362,7 @@ class fatiguelife_gen(rv_continuous):
0.5*(log(2*pi) + 3*log(x)))
def _cdf(self, x, c):
return special.ndtr(1.0 / c * (sqrt(x) - 1.0/sqrt(x)))
return _norm_cdf(1.0 / c * (sqrt(x) - 1.0/sqrt(x)))
def _ppf(self, q, c):
tmp = c*special.ndtri(q)
@ -1545,7 +1541,7 @@ class foldnorm_gen(rv_continuous):
return _norm_pdf(x + c) + _norm_pdf(x-c)
def _cdf(self, x, c):
return special.ndtr(x-c) + special.ndtr(x+c) - 1.0
return _norm_cdf(x-c) + _norm_cdf(x+c) - 1.0
def _stats(self, c):
# Regina C. Elandt, Technometrics 3, 551 (1961)
@ -2061,6 +2057,13 @@ class genextreme_gen(rv_continuous):
return _lazywhere((x == x) & (c != 0), (x, c),
lambda x, c: -expm1(-c * x) / c, x)
def _isf(self, q, c):
x = -log(-special.log1p(-q))
result = _lazywhere((c == 0)*(x == x), (x, c),
f=lambda x, c: x,
f2=lambda x, c: -special.expm1(-c*x)/c)
return result
def _stats(self, c):
g = lambda n: gam(n*c+1)
g1 = g(1)
@ -2087,16 +2090,6 @@ class genextreme_gen(rv_continuous):
ku = where(abs(c) <= (eps)**0.23, 12.0/5.0, ku1-3.0)
return m, v, sk, ku
def _munp(self, n, c):
k = arange(0, n+1)
vals = 1.0/c**n * np.sum(
comb(n, k) * (-1)**k * special.gamma(c*k + 1),
axis=0)
return where(c*n > -1, vals, inf)
def _entropy(self, c):
return _EULER*(1 - c) + 1
def _fitstart(self, data):
d = asarray(data)
# Probability weighted moments
@ -2114,6 +2107,17 @@ class genextreme_gen(rv_continuous):
(exp(gamln(1 + shape)) * (1 - 2 ** (-shape)))
loc = b0 + scale * (expm1(gamln(1 + shape))) / shape
return shape, loc, scale
def _munp(self, n, c):
k = arange(0, n+1)
vals = 1.0/c**n * np.sum(
comb(n, k) * (-1)**k * special.gamma(c*k + 1),
axis=0)
return where(c*n > -1, vals, inf)
def _entropy(self, c):
return _EULER*(1 - c) + 1
genextreme = genextreme_gen(name='genextreme')
@ -2695,7 +2699,7 @@ class halfnorm_gen(rv_continuous):
return 0.5 * np.log(2.0/pi) - x*x/2.0
def _cdf(self, x):
return special.ndtr(x)*2-1.0
return _norm_cdf(x)*2-1.0
def _ppf(self, q):
return special.ndtri((1+q)/2.0)
@ -2852,7 +2856,7 @@ class invgauss_gen(rv_continuous):
%(after_notes)s
When `mu` is too small, evaluating the cumulative density function will be
When `mu` is too small, evaluating the cumulative distribution function will be
inaccurate due to ``cdf(mu -> 0) = inf * 0``.
NaNs are returned for ``mu <= 0.0028``.
@ -3348,9 +3352,18 @@ class lognorm_gen(rv_continuous):
def _cdf(self, x, s):
return _norm_cdf(log(x) / s)
def _logcdf(self, x, s):
return _norm_logcdf(log(x) / s)
def _ppf(self, q, s):
return exp(s * _norm_ppf(q))
def _sf(self, x, s):
return _norm_sf(log(x) / s)
def _logsf(self, x, s):
return _norm_logsf(log(x) / s)
def _stats(self, s):
p = exp(s*s)
mu = sqrt(p)
@ -4546,13 +4559,13 @@ class skew_norm_gen(rv_continuous):
Notes
-----
The pdf is
The pdf is::
skewnorm.pdf(x, a) = 2*norm.pdf(x)*norm.cdf(ax)
`skewnorm` takes ``a`` as a skewness parameter
When a=0 the distribution is identical to a normal distribution.
rvs implements the method of [1].
rvs implements the method of [1]_.
%(after_notes)s
@ -4562,7 +4575,7 @@ class skew_norm_gen(rv_continuous):
References
----------
[1] A. Azzalini and A. Capitanio (1999). Statistical applications of the
.. [1] A. Azzalini and A. Capitanio (1999). Statistical applications of the
multivariate skew-normal distribution. J. Roy. Statist. Soc., B 61, 579-602.
http://azzalini.stat.unipd.it/SN/faq-r.html
"""
@ -4597,6 +4610,56 @@ class skew_norm_gen(rv_continuous):
skewnorm = skew_norm_gen(name='skewnorm')
class trapz_gen(rv_continuous):
"""A trapezoidal continuous random variable.
%(before_notes)s
Notes
-----
The trapezoidal distribution can be represented with an up-sloping line
from ``loc`` to ``(loc + c*scale)``, then constant to ``(loc + d*scale)``
and then downsloping from ``(loc + d*scale)`` to ``(loc+scale)``.
`trapz` takes ``c`` and ``d`` as shape parameters.
%(after_notes)s
The standard form is in the range [0, 1] with c the mode.
The location parameter shifts the start to `loc`.
The scale parameter changes the width from 1 to `scale`.
%(example)s
"""
def _argcheck(self, c, d):
return (c >= 0) & (c <= 1) & (d >= 0) & (d <= 1) & (d >= c)
def _pdf(self, x, c, d):
u = 2 / (d - c + 1)
condlist = [x < c, x <= d, x > d]
choicelist = [u * x / c, u, u * (1 - x) / (1 - d)]
return np.select(condlist, choicelist)
def _cdf(self, x, c, d):
condlist = [x < c, x <= d, x > d]
choicelist = [x**2 / c / (d - c + 1),
(c + 2 * (x - c)) / (d - c + 1),
1 - ((1 - x)**2 / (d - c + 1) / (1 - d))]
return np.select(condlist, choicelist)
def _ppf(self, q, c, d):
qc, qd = self._cdf(c, c, d), self._cdf(d, c, d)
condlist = [q < qc, q <= qd, q > qd]
choicelist = [np.sqrt(q * c * (1 + d - c)),
0.5 * q * (1 + d - c) + 0.5 * c,
1 - sqrt((1 - q) * (d - c + 1) * (1 - d))]
return np.select(condlist, choicelist)
trapz = trapz_gen(a=0.0, b=1.0, name="trapz")
class triang_gen(rv_continuous):
"""A triangular continuous random variable.
@ -4868,13 +4931,17 @@ class vonmises_gen(rv_continuous):
return self._random_state.vonmises(0.0, kappa, size=self._size)
def _pdf(self, x, kappa):
return exp(kappa * cos(x)) / (2*pi*special.i0(kappa))
return exp(kappa * cos(x)) / (2*pi*i0(kappa))
def _cdf(self, x, kappa):
return vonmises_cython.von_mises_cdf(kappa, x)
def _stats_skip(self, kappa):
return 0, None, 0, None
def _entropy(self, kappa):
return (-kappa * i1(kappa) / i0(kappa)
+ np.log(2 * np.pi * i0(kappa)))
vonmises = vonmises_gen(name='vonmises')
vonmises_line = vonmises_gen(a=-np.pi, b=np.pi, name='vonmises_line')

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