"""Frechet or Extreme value distribution type 2."""
import numpy
from scipy import special
from ..baseclass import SimpleDistribution, ShiftScaleDistribution
class frechet(SimpleDistribution):
"""Frechet or Extreme value distribution type 2."""
def __init__(self, c=1):
super(frechet, self).__init__(dict(c=c))
def _pdf(self, x, c):
return c * pow(x, c - 1) * numpy.exp(-pow(x, c))
def _cdf(self, x, c):
return -numpy.expm1(-pow(x, c))
def _ppf(self, q, c):
return pow(-numpy.log1p(-q), 1.0 / c)
def _mom(self, k, c):
return special.gamma(1 - k * 1.0 / c)
def _lower(self, c):
return 0.0
def _upper(self, c):
return pow(35, (1.0 / c))
[docs]class Frechet(ShiftScaleDistribution):
"""
Frechet or Extreme value distribution type 2.
Args:
shape (float, Distribution):
Shape parameter.
scale (float, Distribution):
Scaling parameter.
shift (float, Distribution):
Location parameter.
Examples:
>>> distribution = chaospy.Frechet(3)
>>> distribution
Frechet(3)
>>> 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. , 0.607, 0.799, 0.971, 1.172, 3.271])
>>> numpy.allclose(distribution.fwd(xloc), uloc)
True
>>> distribution.pdf(xloc).round(3)
array([0. , 0.883, 1.15 , 1.132, 0.824, 0. ])
>>> distribution.sample(4).round(3)
array([1.02 , 0.496, 1.442, 0.87 ])
"""
[docs] def __init__(self, shape=1, scale=1, shift=0):
super(Frechet, self).__init__(
dist=frechet(shape),
scale=scale,
shift=shift,
repr_args=[shape],
)