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Merge branch 'master' of https://github.com/wafo-project/pywafo.git

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master
pbrod 9 years ago
parent 9a87ed63b7 f8d1afb93b
commit cced4aeb0b
2 changed files with 237 additions and 203 deletions
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wafo/stats/_continuous_distns.py
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@ -13,7 +13,8 @@ from scipy import optimize
from scipy import integrate from scipy import integrate
from scipy.special import (gammaln as gamln, gamma as gam, boxcox, boxcox1p, from scipy.special import (gammaln as gamln, gamma as gam, boxcox, boxcox1p,
inv_boxcox, inv_boxcox1p, erfc, chndtr, chndtrix, 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, from numpy import (where, arange, putmask, ravel, shape,
log, sqrt, exp, arctanh, tan, sin, arcsin, arctan, log, sqrt, exp, arctanh, tan, sin, arcsin, arctan,
@ -31,13 +32,12 @@ except:
from scipy.stats._tukeylambda_stats import (tukeylambda_variance as _tlvar, from scipy.stats._tukeylambda_stats import (tukeylambda_variance as _tlvar,
tukeylambda_kurtosis as _tlkurt) tukeylambda_kurtosis as _tlkurt)
from ._distn_infrastructure import ( from wafo.stats._distn_infrastructure import (
rv_continuous, valarray, _skew, _kurtosis, # @UnresolvedImport rv_continuous, valarray, _skew, _kurtosis, _lazywhere,
_lazywhere, _ncx2_log_pdf, _ncx2_pdf, _ncx2_cdf, # @UnresolvedImport _ncx2_log_pdf, _ncx2_pdf, _ncx2_cdf, get_distribution_names,
get_distribution_names, # @UnresolvedImport
) )
from ._constants import _XMIN, _EULER, _ZETA3, _XMAX, _LOGXMAX, _EPS from wafo.stats._constants import _XMIN, _EULER, _ZETA3, _XMAX, _LOGXMAX, _EPS
## Kolmogorov-Smirnov one-sided and two-sided test statistics ## Kolmogorov-Smirnov one-sided and two-sided test statistics
@ -89,24 +89,16 @@ def _norm_logpdf(x):
return -x**2 / 2.0 - _norm_pdf_logC 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): def _norm_ppf(q):
return special.ndtri(q) return special.ndtri(q)
def _norm_sf(x): def _norm_sf(x):
return special.ndtr(-x) return _norm_cdf(-x)
def _norm_logsf(x): def _norm_logsf(x):
return special.log_ndtr(-x) return _norm_logcdf(-x)
def _norm_isf(q): def _norm_isf(q):
@ -127,6 +119,10 @@ class norm_gen(rv_continuous):
norm.pdf(x) = exp(-x**2/2)/sqrt(2*pi) 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 %(after_notes)s
%(example)s %(example)s
@ -220,13 +216,13 @@ class alpha_gen(rv_continuous):
""" """
def _pdf(self, x, a): 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): 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): 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): def _ppf(self, q, a):
return 1.0/asarray(a-special.ndtri(q*special.ndtr(a))) return 1.0/asarray(a-special.ndtri(q*special.ndtr(a)))
@ -605,13 +601,13 @@ class bradford_gen(rv_continuous):
""" """
def _pdf(self, x, c): def _pdf(self, x, c):
return c / (c * x + 1.0) / log1p(c) return c * exp(-log1p(c * x)) / log1p(c)
def _cdf(self, x, c): def _cdf(self, x, c):
return log1p(c * x) / log1p(c) return log1p(c * x) / log1p(c)
def _ppf(self, q, c): def _ppf(self, q, c):
return ((1.0+c)**q-1)/c return expm1(q * log1p(c))/c # ((1.0+c)**q-1)/c
def _stats(self, c, moments='mv'): def _stats(self, c, moments='mv'):
k = log1p(c) k = log1p(c)
@ -1124,15 +1120,6 @@ class expon_gen(rv_continuous):
%(example)s %(example)s
""" """
def _link(self, x, logSF, phat, ix):
if ix == 1:
return - (x - phat[0]) / logSF
elif ix == 0:
return x + phat[1] * logSF
else:
raise IndexError('Index to the fixed parameter is out of bounds')
def _rvs(self): def _rvs(self):
return self._random_state.standard_exponential(self._size) return self._random_state.standard_exponential(self._size)
@ -1221,12 +1208,12 @@ class exponnorm_gen(rv_continuous):
def _cdf(self, x, K): def _cdf(self, x, K):
invK = 1.0 / K invK = 1.0 / K
expval = invK * (0.5 * invK - x) 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): def _sf(self, x, K):
invK = 1.0 / K invK = 1.0 / K
expval = invK * (0.5 * invK - x) 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): def _stats(self, K):
K2 = K * K K2 = K * K
@ -1366,7 +1353,7 @@ class fatiguelife_gen(rv_continuous):
0.5*(log(2*pi) + 3*log(x))) 0.5*(log(2*pi) + 3*log(x)))
def _cdf(self, x, c): 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): def _ppf(self, q, c):
tmp = c*special.ndtri(q) tmp = c*special.ndtri(q)
@ -1545,7 +1532,7 @@ class foldnorm_gen(rv_continuous):
return _norm_pdf(x + c) + _norm_pdf(x-c) return _norm_pdf(x + c) + _norm_pdf(x-c)
def _cdf(self, 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): def _stats(self, c):
# Regina C. Elandt, Technometrics 3, 551 (1961) # Regina C. Elandt, Technometrics 3, 551 (1961)
@ -1597,17 +1584,6 @@ class frechet_r_gen(rv_continuous):
%(example)s %(example)s
""" """
def _link(self, x, logSF, phat, ix):
if ix == 0:
phati = log(-logSF) / log((x - phat[1]) / phat[2])
elif ix == 1:
phati = x - phat[2] * (-logSF) ** (1. / phat[0])
elif ix == 2:
phati = (x - phat[1]) / (-logSF) ** (1. / phat[0])
else:
raise IndexError('Index to the fixed parameter is out of bounds')
return phati
def _pdf(self, x, c): def _pdf(self, x, c):
return c*pow(x, c-1)*exp(-pow(x, c)) return c*pow(x, c-1)*exp(-pow(x, c))
@ -1736,14 +1712,6 @@ class genlogistic_gen(rv_continuous):
genlogistic = genlogistic_gen(name='genlogistic') genlogistic = genlogistic_gen(name='genlogistic')
def log1pxdx(x):
'''Computes Log(1+x)/x
'''
xd = where((x == 0) | (x == inf), 1.0, x) # avoid 0/0 or inf/inf
y = where(x == 0, 1.0, log1p(x) / xd)
return where(x == inf, 0.0, y)
class genpareto_gen(rv_continuous): class genpareto_gen(rv_continuous):
"""A generalized Pareto continuous random variable. """A generalized Pareto continuous random variable.
@ -1774,33 +1742,6 @@ class genpareto_gen(rv_continuous):
%(example)s %(example)s
""" """
def _link(self, x, logSF, phat, ix):
# Reference
# Stuart Coles (2004)
# "An introduction to statistical modelling of extreme values".
# Springer series in statistics
c, loc, scale = phat
if ix == 2:
# Reorganizing w.r.t.scale, Eq. 4.13 and 4.14, pp 81 in
# Coles (2004) gives
# link = -(x-loc)*c/expm1(-c*logSF)
if c != 0.0:
phati = (x - loc) * c / expm1(-c * logSF)
else:
phati = -(x - loc) / logSF
elif ix == 1:
if c != 0:
phati = x + scale * expm1(c * logSF) / c
else:
phati = x + scale * logSF
elif ix == 0:
raise NotImplementedError(
'link(x,logSF,phat,i) where i=0 is not implemented!')
else:
raise IndexError('Index to the fixed parameter is out of bounds')
return phati
def _argcheck(self, c): def _argcheck(self, c):
c = asarray(c) c = asarray(c)
self.b = _lazywhere(c < 0, (c,), self.b = _lazywhere(c < 0, (c,),
@ -1844,57 +1785,6 @@ class genpareto_gen(rv_continuous):
scale = m * ((m / s) ** 2 + 1) / 2 scale = m * ((m / s) ** 2 + 1) / 2
return shape, loc, scale return shape, loc, scale
def hessian_nnlf(self, theta, x, eps=None):
try:
loc = theta[-2]
scale = theta[-1]
args = tuple(theta[:-2])
except IndexError:
raise ValueError("Not enough input arguments.")
if not self._argcheck(*args) or scale <= 0:
return inf
x = asarray((x - loc) / scale)
cond0 = (x <= self.a) | (x >= self.b)
if any(cond0):
np = self.numargs + 2
return valarray((np, np), value=nan)
eps = _EPS
c = args[0]
n = len(x)
if abs(c) > eps:
cx = c * x
sumlog1pcx = sum(log1p(cx))
# LL = n*log(scale) + (1-1/k)*sumlog1mkxn
r = x / (1.0 + cx)
sumix = sum(1.0 / (1.0 + cx) ** 2.0)
sumr = sum(r)
sumr2 = sum(r ** 2.0)
H11 = -2 * sumlog1pcx / c ** 3 + 2 * \
sumr / c ** 2 + (1.0 + 1.0 / c) * sumr2
H22 = c * (c + 1) * sumix / scale ** 2.0
H33 = (n - 2 * (c + 1) * sumr +
c * (c + 1) * sumr2) / scale ** 2.0
H12 = -sum((1 - x) / ((1 + cx) ** 2.0)) / scale
H23 = -(c + 1) * sumix / scale ** 2.0
H13 = -(sumr - (c + 1) * sumr2) / scale
else: # c == 0
sumx = sum(x)
# LL = n*log(scale) + sumx;
sumx2 = sum(x ** 2.0)
H11 = -(2 / 3) * sum(x ** 3.0) + sumx2
H22 = 0.0
H12 = -(n - sum(x)) / scale
H23 = -n * 1.0 / scale ** 2.0
H33 = (n - 2 * sumx) / scale ** 2.0
H13 = -(sumx - sumx2) / scale
# Hessian matrix
H = [[H11, H12, H13], [H12, H22, H23], [H13, H23, H33]]
return asarray(H)
def __stats(self, c): def __stats(self, c):
# return None,None,None,None # return None,None,None,None
k = -c k = -c
@ -1962,24 +1852,8 @@ class genexpon_gen(rv_continuous):
%(example)s %(example)s
""" """
def _link(self, x, logSF, phat, ix):
_a, b, c, loc, scale = phat
xn = (x - loc) / scale
fact1 = (xn + expm1(-c * xn) / c)
if ix == 0:
phati = b * fact1 + logSF
elif ix == 1:
phati = (phat[0] - logSF) / fact1
elif ix in [2, 3, 4]:
raise NotImplementedError('Only implemented for index in [0,1]!')
else:
raise IndexError('Index to the fixed parameter is out of bounds')
return phati
def _pdf(self, x, a, b, c): def _pdf(self, x, a, b, c):
return (a + b*(-special.expm1(-c*x)))*exp((-a-b)*x + return (a + b*(-special.expm1(-c*x))) * exp((-a-b)*x +
b*(-special.expm1(-c*x))/c) b*(-special.expm1(-c*x))/c)
def _cdf(self, x, a, b, c): def _cdf(self, x, a, b, c):
@ -2030,28 +1904,25 @@ class genextreme_gen(rv_continuous):
return exp(self._logpdf(x, c)) return exp(self._logpdf(x, c))
def _logpdf(self, x, c): def _logpdf(self, x, c):
x1 = where((c == 0) & (x == inf), 0.0, x) cx = _lazywhere((c != 0)*(x == x), (x, c), lambda x, c: c*x, 0.0)
cx = c * x1 logex2 = special.log1p(-cx)
cond1 = (c == 0) * (x == x) logpex2 = self._loglogcdf(x, c)
logex2 = where(cond1, 0.0, log1p(-cx))
logpex2 = -x * log1pxdx(-cx)
# logpex2 = where(cond1,-x, logex2/c)
pex2 = exp(logpex2) pex2 = exp(logpex2)
# Handle special cases # Handle special cases
logpdf = where( putmask(logpex2, (c == 0) & (x == -inf), 0.0)
(cx == 1) | (cx == -inf), -inf, -pex2 + logpex2 - logex2) logpdf = where((cx == 1) | (cx == -inf), -inf, -pex2+logpex2-logex2)
putmask(logpdf, (c == 1) & (x == 1), 0.0) putmask(logpdf, (c == 1) & (x == 1), 0.0)
return logpdf return logpdf
def _cdf(self, x, c): def _cdf(self, x, c):
return exp(self._logcdf(x, c)) return exp(self._logcdf(x, c))
def _loglogcdf(self, x, c):
return _lazywhere((c != 0) & (x == x), (x, c),
lambda x, c: special.log1p(-c * x)/c, -x)
def _logcdf(self, x, c): def _logcdf(self, x, c):
x1 = where((c == 0) & (x == inf), 0.0, x) return -exp(self._loglogcdf(x, c))
cx = c * x1
loglogcdf = -x * log1pxdx(-cx)
# loglogcdf = where((c==0)*(x==x),-x,log1p(-cx)/c)
return -exp(loglogcdf)
def _sf(self, x, c): def _sf(self, x, c):
return -expm1(self._logcdf(x, c)) return -expm1(self._logcdf(x, c))
@ -2061,6 +1932,11 @@ class genextreme_gen(rv_continuous):
return _lazywhere((x == x) & (c != 0), (x, c), return _lazywhere((x == x) & (c != 0), (x, c),
lambda x, c: -expm1(-c * x) / c, x) lambda x, c: -expm1(-c * x) / c, x)
def _isf(self, q, c):
x = -log(-special.log1p(-q))
return _lazywhere((x == x) & (c != 0), (x, c),
lambda x, c: -expm1(-c * x) / c, x)
def _stats(self, c): def _stats(self, c):
g = lambda n: gam(n*c+1) g = lambda n: gam(n*c+1)
g1 = g(1) g1 = g(1)
@ -2087,16 +1963,6 @@ class genextreme_gen(rv_continuous):
ku = where(abs(c) <= (eps)**0.23, 12.0/5.0, ku1-3.0) ku = where(abs(c) <= (eps)**0.23, 12.0/5.0, ku1-3.0)
return m, v, sk, ku 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): def _fitstart(self, data):
d = asarray(data) d = asarray(data)
# Probability weighted moments # Probability weighted moments
@ -2114,6 +1980,17 @@ class genextreme_gen(rv_continuous):
(exp(gamln(1 + shape)) * (1 - 2 ** (-shape))) (exp(gamln(1 + shape)) * (1 - 2 ** (-shape)))
loc = b0 + scale * (expm1(gamln(1 + shape))) / shape loc = b0 + scale * (expm1(gamln(1 + shape))) / shape
return shape, loc, scale 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') genextreme = genextreme_gen(name='genextreme')
@ -2566,6 +2443,12 @@ class gumbel_l_gen(rv_continuous):
def _logpdf(self, x): def _logpdf(self, x):
return x - exp(x) return x - exp(x)
def _logsf(self, x):
return -exp(x)
def _sf(self, x):
return exp(-exp(x))
def _cdf(self, x): def _cdf(self, x):
return -expm1(-exp(x)) return -expm1(-exp(x))
@ -2695,7 +2578,7 @@ class halfnorm_gen(rv_continuous):
return 0.5 * np.log(2.0/pi) - x*x/2.0 return 0.5 * np.log(2.0/pi) - x*x/2.0
def _cdf(self, x): def _cdf(self, x):
return special.ndtr(x)*2-1.0 return _norm_cdf(x)*2-1.0
def _ppf(self, q): def _ppf(self, q):
return special.ndtri((1+q)/2.0) return special.ndtri((1+q)/2.0)
@ -2852,7 +2735,7 @@ class invgauss_gen(rv_continuous):
%(after_notes)s %(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``. inaccurate due to ``cdf(mu -> 0) = inf * 0``.
NaNs are returned for ``mu <= 0.0028``. NaNs are returned for ``mu <= 0.0028``.
@ -3206,6 +3089,9 @@ class logistic_gen(rv_continuous):
def _ppf(self, q): def _ppf(self, q):
return -log1p(-q) + log(q) return -log1p(-q) + log(q)
def _isf(self, q):
return log1p(-q) - log(q)
def _stats(self): def _stats(self):
return 0, pi*pi/3.0, 0, 6.0/5.0 return 0, pi*pi/3.0, 0, 6.0/5.0
@ -3348,9 +3234,18 @@ class lognorm_gen(rv_continuous):
def _cdf(self, x, s): def _cdf(self, x, s):
return _norm_cdf(log(x) / s) return _norm_cdf(log(x) / s)
def _logcdf(self, x, s):
return _norm_logcdf(log(x) / s)
def _ppf(self, q, s): def _ppf(self, q, s):
return exp(s * _norm_ppf(q)) 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): def _stats(self, s):
p = exp(s*s) p = exp(s*s)
mu = sqrt(p) mu = sqrt(p)
@ -4239,15 +4134,6 @@ class rayleigh_gen(rv_continuous):
%(example)s %(example)s
""" """
def _link(self, x, logSF, phat, ix):
if ix == 1:
return x - phat[0] / sqrt(-2.0 * logSF)
elif ix == 0:
return x - phat[1] * sqrt(-2.0 * logSF)
else:
raise IndexError('Index to the fixed parameter is out of bounds')
def _rvs(self): def _rvs(self):
return chi.rvs(2, size=self._size, random_state=self._random_state) return chi.rvs(2, size=self._size, random_state=self._random_state)
@ -4256,7 +4142,8 @@ class rayleigh_gen(rv_continuous):
def _logpdf(self, r): def _logpdf(self, r):
rr2 = r * r / 2.0 rr2 = r * r / 2.0
return where(rr2 == inf, - rr2, log(r) - rr2) return _lazywhere(rr2 != inf, (r, rr2), lambda r, rr2: log(r) - rr2,
-rr2)
def _cdf(self, r): def _cdf(self, r):
return -special.expm1(-0.5 * r**2) return -special.expm1(-0.5 * r**2)
@ -4267,6 +4154,9 @@ class rayleigh_gen(rv_continuous):
def _sf(self, r): def _sf(self, r):
return exp(-0.5 * r**2) return exp(-0.5 * r**2)
def _logsf(self, r):
return -0.5 * r**2
def _isf(self, q): def _isf(self, q):
return sqrt(-2 * log(q)) return sqrt(-2 * log(q))
@ -4301,18 +4191,6 @@ class truncrayleigh_gen(rv_continuous):
def _argcheck(self, c): def _argcheck(self, c):
return (c >= 0) return (c >= 0)
def _link(self, x, logSF, phat, ix):
c, loc, scale = phat
if ix == 2:
return x - loc / (sqrt(c * c - 2 * logSF) - c)
elif ix == 1:
return x - scale * (sqrt(c * c - 2 * logSF) - c)
elif ix == 0:
xn = (x - loc) / scale
return - 2 * logSF / xn - xn / 2.0
else:
raise IndexError('Index to the fixed parameter is out of bounds')
def _fitstart(self, data, args=None): def _fitstart(self, data, args=None):
if args is None: if args is None:
args = (0.0,) * self.numargs args = (0.0,) * self.numargs
@ -4546,13 +4424,13 @@ class skew_norm_gen(rv_continuous):
Notes Notes
----- -----
The pdf is The pdf is::
skewnorm.pdf(x, a) = 2*norm.pdf(x)*norm.cdf(ax) skewnorm.pdf(x, a) = 2*norm.pdf(x)*norm.cdf(ax)
`skewnorm` takes ``a`` as a skewness parameter `skewnorm` takes ``a`` as a skewness parameter
When a=0 the distribution is identical to a normal distribution. 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 %(after_notes)s
@ -4562,7 +4440,7 @@ class skew_norm_gen(rv_continuous):
References 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. multivariate skew-normal distribution. J. Roy. Statist. Soc., B 61, 579-602.
http://azzalini.stat.unipd.it/SN/faq-r.html http://azzalini.stat.unipd.it/SN/faq-r.html
""" """
@ -4597,6 +4475,56 @@ class skew_norm_gen(rv_continuous):
skewnorm = skew_norm_gen(name='skewnorm') 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): class triang_gen(rv_continuous):
"""A triangular continuous random variable. """A triangular continuous random variable.
@ -4868,13 +4796,17 @@ class vonmises_gen(rv_continuous):
return self._random_state.vonmises(0.0, kappa, size=self._size) return self._random_state.vonmises(0.0, kappa, size=self._size)
def _pdf(self, x, kappa): 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): def _cdf(self, x, kappa):
return vonmises_cython.von_mises_cdf(kappa, x) return vonmises_cython.von_mises_cdf(kappa, x)
def _stats_skip(self, kappa): def _stats_skip(self, kappa):
return 0, None, 0, None 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 = vonmises_gen(name='vonmises')
vonmises_line = vonmises_gen(a=-np.pi, b=np.pi, name='vonmises_line') vonmises_line = vonmises_gen(a=-np.pi, b=np.pi, name='vonmises_line')
@ -5098,3 +5030,9 @@ pairs = list(globals().items())
_distn_names, _distn_gen_names = get_distribution_names(pairs, rv_continuous) _distn_names, _distn_gen_names = get_distribution_names(pairs, rv_continuous)
__all__ = _distn_names + _distn_gen_names __all__ = _distn_names + _distn_gen_names
if __name__ == '__main__':
v = genextreme.logpdf(np.inf, 0)
v2 = genextreme.logpdf(-np.inf, 0)
v2 = genextreme.logpdf(-100, 0)

100
wafo/stats/estimation.py
Unescape Escape View File

@ -21,19 +21,115 @@ from scipy.linalg import pinv2
from scipy import optimize from scipy import optimize
import numpy as np import numpy as np
from numpy import (alltrue, arange, zeros, log, sqrt, exp, from numpy import (alltrue, arange, zeros, log, sqrt, exp, expm1,
atleast_1d, any, asarray, nan, pi, isfinite) atleast_1d, any, asarray, nan, pi, isfinite)
from numpy import flatnonzero as nonzero from numpy import flatnonzero as nonzero
__all__ = ['Profile', 'FitDistribution'] __all__ = ['Profile', 'FitDistribution']
floatinfo = np.finfo(float) floatinfo = np.finfo(float)
arr = asarray arr = asarray
all = alltrue # @ReservedAssignment all = alltrue # @ReservedAssignment
def _expon_link(x, logSF, phat, ix):
if ix == 1:
return - (x - phat[0]) / logSF
elif ix == 0:
return x + phat[1] * logSF
else:
raise IndexError('Index to the fixed parameter is out of bounds')
def _weibull_min_link(x, logSF, phat, ix):
if ix == 0:
phati = log(-logSF) / log((x - phat[1]) / phat[2])
elif ix == 1:
phati = x - phat[2] * (-logSF) ** (1. / phat[0])
elif ix == 2:
phati = (x - phat[1]) / (-logSF) ** (1. / phat[0])
else:
raise IndexError('Index to the fixed parameter is out of bounds')
return phati
def _genpareto_link(x, logSF, phat, ix):
# Reference
# Stuart Coles (2004)
# "An introduction to statistical modelling of extreme values".
# Springer series in statistics
c, loc, scale = phat
if ix == 2:
# Reorganizing w.r.t.scale, Eq. 4.13 and 4.14, pp 81 in
# Coles (2004) gives
# link = -(x-loc)*c/expm1(-c*logSF)
if c != 0.0:
phati = (x - loc) * c / expm1(-c * logSF)
else:
phati = -(x - loc) / logSF
elif ix == 1:
if c != 0:
phati = x + scale * expm1(c * logSF) / c
else:
phati = x + scale * logSF
elif ix == 0:
raise NotImplementedError(
'link(x,logSF,phat,i) where i=0 is not implemented!')
else:
raise IndexError('Index to the fixed parameter is out of bounds')
return phati
def _genexpon_link(x, logSF, phat, ix):
_a, b, c, loc, scale = phat
xn = (x - loc) / scale
fact1 = (xn + expm1(-c * xn) / c)
if ix == 0:
phati = b * fact1 + logSF
elif ix == 1:
phati = (phat[0] - logSF) / fact1
elif ix in [2, 3, 4]:
raise NotImplementedError('Only implemented for index in [0,1]!')
else:
raise IndexError('Index to the fixed parameter is out of bounds')
return phati
def _rayleigh_link(x, logSF, phat, ix):
if ix == 1:
return x - phat[0] / sqrt(-2.0 * logSF)
elif ix == 0:
return x - phat[1] * sqrt(-2.0 * logSF)
else:
raise IndexError('Index to the fixed parameter is out of bounds')
def _trunclayleigh_link(x, logSF, phat, ix):
c, loc, scale = phat
if ix == 2:
return x - loc / (sqrt(c * c - 2 * logSF) - c)
elif ix == 1:
return x - scale * (sqrt(c * c - 2 * logSF) - c)
elif ix == 0:
xn = (x - loc) / scale
return - 2 * logSF / xn - xn / 2.0
else:
raise IndexError('Index to the fixed parameter is out of bounds')
LINKS = dict(expon=_expon_link,
weibull_min=_weibull_min_link,
frechet_r=_weibull_min_link,
genpareto=_genpareto_link,
genexpon=_genexpon_link,
rayleigh=_rayleigh_link,
trunclayleigh=_trunclayleigh_link)
def chi2isf(p, df): def chi2isf(p, df):
return special.chdtri(df, p) return special.chdtri(df, p)
@ -197,7 +293,7 @@ class Profile(object):
self.profile_par = not (self.profile_x or self.profile_logSF) self.profile_par = not (self.profile_x or self.profile_logSF)
if self.link is None: if self.link is None:
self.link = self.fit_dist.dist.link self.link = LINKS[self.fit_dist.dist.name]
if self.profile_par: if self.profile_par:
self._local_link = self._par_link self._local_link = self._par_link
self.xlabel = 'phat(%d)' % self.i_fixed self.xlabel = 'phat(%d)' % self.i_fixed

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