"""Generalized gamma distribution."""
import numpy
from scipy import special
from ..baseclass import SimpleDistribution, ShiftScaleDistribution
class generalized_gamma(SimpleDistribution):
"""Generalized gamma distribution."""
def __init__(self, a, c):
super(generalized_gamma, self).__init__(dict(a=a, c=c))
def _pdf(self, x, a, c):
return abs(c) * numpy.exp(
(c * a - 1) * numpy.log(numpy.clip(x, 1e-15, None))
- x**c
- special.gammaln(a)
)
def _cdf(self, x, a, c):
val = special.gammainc(a, x**c)
cond = c + 0 * val
return numpy.where(cond > 0, val, 1 - val)
def _ppf(self, q, a, c):
val = numpy.where(c > 0, q, 1 - q)
return special.gammaincinv(a, val) ** (1.0 / c)
def _lower(self, a, c):
return 0.0
def _upper(self, a, c):
cond = c > 0
val = numpy.where(cond, 1 - 1e-15, 1e-15)
return special.gammaincinv(a, val) ** (1.0 / c)
def _mom(self, k, a, c):
return special.gamma((c + k) * 1.0 / a) / special.gamma(c * 1.0 / a)
[docs]class GeneralizedGamma(ShiftScaleDistribution):
"""
Generalized gamma distribution
Args:
shape1 (float, Distribution):
Shape parameter 1
shape2 (float, Distribution):
Shape parameter 2
scale (float, Distribution):
Scaling parameter
shift (float, Distribution):
Location parameter
Examples:
>>> distribution = chaospy.GeneralizedGamma(1.5, 15)
>>> distribution
GeneralizedGamma(1.5, 15)
>>> uloc = numpy.linspace(0, 1, 6)
>>> uloc
array([0. , 0.2, 0.4, 0.6, 0.8, 1. ])
>>> xloc = distribution.inv(uloc)
>>> xloc.round(3)
array([0. , 0.955, 0.995, 1.026, 1.058, 1.271])
>>> numpy.allclose(distribution.fwd(xloc), uloc)
True
>>> distribution.pdf(xloc).round(3)
array([0. , 3.82 , 6.033, 6.76 , 5.555, 0. ])
>>> distribution.sample(4).round(3)
array([1.034, 0.928, 1.095, 1.009])
>>> distribution.mom(1).round(3)
4.591
"""
[docs] def __init__(self, shape1, shape2, scale=1, shift=0):
super(GeneralizedGamma, self).__init__(
dist=generalized_gamma(shape1, shape2),
scale=scale,
shift=shift,
repr_args=[shape1, shape2],
)