"""Generalized half-logistic distribution."""
import numpy
from scipy import special
from ..baseclass import SimpleDistribution, ShiftScaleDistribution
class generalized_half_logistic(SimpleDistribution):
"""Generalized half-logistic distribution."""
def __init__(self, c=1):
super(generalized_half_logistic, self).__init__(dict(c=c))
def _pdf(self, x, c):
limit = 1.0 / c
tmp = 1 - c * x
tmp0 = tmp ** (limit - 1)
tmp2 = tmp0 * tmp
return 2 * tmp0 / (1 + tmp2) ** 2
def _cdf(self, x, c):
limit = 1.0 / c
tmp = 1 - c * x
tmp2 = tmp ** (limit)
return (1.0 - tmp2) / (1 + tmp2)
def _ppf(self, q, c):
return 1.0 / c * (1 - ((1.0 - q) / (1.0 + q)) ** c)
def _lower(self, c):
return 0.0
def _upper(self, c):
return 1 / numpy.where(c < 10**-10, 10**-10, c)
[docs]class GeneralizedHalfLogistic(ShiftScaleDistribution):
"""
Generalized half-logistic distribution
Args:
shape (float, Distribution):
Shape parameter
scale (float, Distribution):
Scaling parameter
shift (float, Distribution):
Location parameter
Examples:
>>> distribution = chaospy.GeneralizedHalfLogistic(0.5)
>>> distribution
GeneralizedHalfLogistic(0.5)
>>> 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. , 0.367, 0.691, 1. , 1.333, 2. ])
>>> numpy.allclose(distribution.fwd(xloc), uloc)
True
>>> distribution.pdf(xloc).round(3)
array([0.5 , 0.588, 0.642, 0.64 , 0.54 , 0. ])
>>> distribution.sample(4).round(3)
array([1.085, 0.218, 1.681, 0.818])
"""
[docs] def __init__(self, shape, scale=1, shift=0):
super(GeneralizedHalfLogistic, self).__init__(
dist=generalized_half_logistic(shape),
scale=scale,
shift=shift,
repr_args=[shape],
)