"""Inverse Gamma distribution."""
import numpy
from scipy import special
from ..baseclass import SimpleDistribution, ShiftScaleDistribution
class inverse_gamma(SimpleDistribution):
def __init__(self, a):
super(inverse_gamma, self).__init__(dict(a=a))
def _lower(self, a):
return 0.0
def _upper(self, a):
return 1.0 / special.gammainccinv(a, 1 - 1e-16)
def _pdf(self, x, a):
x_ = numpy.where(x, x, 1)
return numpy.where(
x, x_ ** (-a - 1) * numpy.exp(-1.0 / x_) / special.gamma(a), 0
)
def _cdf(self, x, a):
return numpy.where(x, special.gammaincc(a, 1.0 / numpy.where(x, x, 1)), 0)
def _ppf(self, q, a):
return 1.0 / special.gammainccinv(a, q)
def _mom(self, k, a):
if k > a:
return self._upper(a)
return 1.0 / numpy.prod(a - numpy.arange(1, k.item() + 1))
[docs]class InverseGamma(ShiftScaleDistribution):
"""
Inverse-Gamma distribution.
Args:
shape (float, Distribution):
Shape parameter. a>0.
scale (float, Distribution):
Scale parameter. scale!=0
shift (float, Distribution):
Location of the lower bound.
Examples:
>>> distribution = chaospy.InverseGamma(shape=10)
>>> distribution
InverseGamma(10)
>>> 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. , 0.08 , 0.095, 0.112, 0.137, 8.608])
>>> numpy.allclose(distribution.fwd(xloc), uloc)
True
>>> distribution.pdf(xloc).round(3)
array([ 0. , 11.928, 12.963, 10.441, 5.808, 0. ])
>>> distribution.sample(4).round(3)
array([0.118, 0.072, 0.185, 0.102])
>>> distribution.mom([1, 2, 3]).round(3)
array([0.111, 0.014, 0.002])
"""
[docs] def __init__(self, shape, scale=1, shift=0):
super(InverseGamma, self).__init__(
dist=inverse_gamma(shape),
scale=scale,
shift=shift,
repr_args=[shape],
)