"""Weibull Distribution."""
import numpy
from scipy import special
from ..baseclass import SimpleDistribution, ShiftScaleDistribution
class weibull(SimpleDistribution):
"""Weibull Distribution."""
def __init__(self, a=1):
super(weibull, self).__init__(dict(a=a))
def _pdf(self, x, a):
return a * x ** (a - 1) * numpy.e ** (-(x**a))
def _cdf(self, x, a):
return 1 - numpy.e ** (-(x**a))
def _ppf(self, q, a):
return (-numpy.log(1 - q + 1 * (q == 1))) ** (1.0 / a) * (q != 1) + 30.0 ** (
1.0 / a
) * (q == 1)
def _mom(self, k, a):
return special.gamma(1.0 + k * 1.0 / a)
def _lower(self, a):
return 0.0
def _upper(self, a):
return 30.0 ** (1.0 / a)
[docs]class Weibull(ShiftScaleDistribution):
"""
Weibull Distribution
Args:
shape (float, Distribution):
Shape parameter.
scale (float, Distribution):
Scale parameter.
shift (float, Distribution):
Location of lower bound.
Examples:
>>> distribution = chaospy.Weibull(2)
>>> distribution
Weibull(2)
>>> 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. , 0.472, 0.715, 0.957, 1.269, 5.477])
>>> numpy.allclose(distribution.fwd(xloc), uloc)
True
>>> distribution.pdf(xloc).round(3)
array([0. , 0.756, 0.858, 0.766, 0.507, 0. ])
>>> distribution.sample(4).round(3)
array([1.03 , 0.35 , 1.732, 0.811])
>>> distribution.mom(1).round(4)
0.8862
"""
[docs] def __init__(self, shape=1, scale=1, shift=0):
super(Weibull, self).__init__(
dist=weibull(shape),
scale=scale,
shift=shift,
repr_args=[shape],
)