"""Exponential power distribution."""
import numpy
from ..baseclass import SimpleDistribution, ShiftScaleDistribution
class exponential_power(SimpleDistribution):
"""Exponential power distribution."""
def __init__(self, b=1):
super(exponential_power, self).__init__(dict(b=b))
def _pdf(self, x, b):
xbm1 = x ** (b - 1.0)
xb = xbm1 * x
return numpy.exp(1) * b * xbm1 * numpy.exp(xb - numpy.exp(xb))
def _cdf(self, x, b):
return -numpy.expm1(-numpy.expm1(x**b))
def _ppf(self, q, b):
return pow(numpy.log1p(-numpy.log1p(-q)), 1.0 / b)
def _lower(self, b):
del b
return 0.0
def _upper(self, b):
return 3.6 ** (1.0 / b)
[docs]class ExponentialPower(ShiftScaleDistribution):
"""
Exponential power distribution.
Also known as Generalized error distribution and Generalized normal
distribution version 1.
Args:
shape (float, Distribution):
Shape parameter
scale (float, Distribution):
Scaling parameter
shift (float, Distribution):
Location parameter
Examples:
>>> distribution = chaospy.ExponentialPower(1.5)
>>> distribution
ExponentialPower(1.5)
>>> 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. , 0.344, 0.554, 0.751, 0.973, 2.349])
>>> numpy.allclose(distribution.fwd(xloc), uloc)
True
>>> distribution.pdf(xloc).round(3)
array([0. , 0.86 , 1.012, 0.996, 0.772, 0. ])
>>> distribution.sample(4).round(3)
array([0.805, 0.237, 1.243, 0.635])
"""
[docs] def __init__(self, shape=1, scale=1, shift=0):
super(ExponentialPower, self).__init__(
dist=exponential_power(shape),
scale=scale,
shift=shift,
repr_args=[shape],
)