"""Generalized exponential distribution."""
import numpy
from scipy import special
from ..baseclass import Dist
from ..operators.addition import Add
class generalized_exponential(Dist):
"""Generalized exponential distribution."""
def __init__(self, a=1, b=1, c=1):
Dist.__init__(self, a=a, b=b, c=c)
def _pdf(self, x, a, b, c):
return (a+b*(-numpy.expm1(-c*x)))*numpy.exp((-a-b)*x+b*(-numpy.expm1(-c*x))/c)
def _cdf(self, x, a, b, c):
output = -numpy.expm1((-a-b)*x + b*(-numpy.expm1(-c*x))/c)
output = numpy.where(x > 0, output, 0)
return output
def _lower(self, a, b, c):
return 0.
def _upper(self, a, b, c):
return 10**10
class GeneralizedExponential(Add):
"""
Generalized exponential distribution.
Args:
a (float, Dist):
First shape parameter
b (float, Dist):
Second shape parameter
c (float, Dist):
Third shape parameter
scale (float, Dist):
Scaling parameter
shift (float, Dist):
Location parameter
Note:
"An Extension of Marshall and Olkin's Bivariate Exponential Distribution",
H.K. Ryu, Journal of the American Statistical Association, 1993.
"The Exponential Distribution: Theory, Methods and Applications",
N. Balakrishnan, Asit P. Basu.
Examples:
>>> distribution = chaospy.GeneralizedExponential(3, 2, 2, 2, 2)
>>> distribution
GeneralizedExponential(a=3, b=2, c=2, scale=2, shift=2)
>>> q = numpy.linspace(0, 1, 6)[1:-1]
>>> distribution.inv(q).round(4)
array([2.1423, 2.3113, 2.5314, 2.8774])
>>> distribution.fwd(distribution.inv(q)).round(4)
array([0.2, 0.4, 0.6, 0.8])
>>> distribution.pdf(distribution.inv(q)).round(4)
array([1.3061, 1.0605, 0.7649, 0.4168])
>>> distribution.sample(4).round(4)
array([3.3106, 2.0498, 3.3575, 2.7079])
"""
def __init__(self, a=1, b=1, c=1, scale=1, shift=0):
self._repr = {"a": a, "b": b, "c": c, "scale": scale, "shift": shift}
Add.__init__(
self, left=generalized_exponential(a, b, c)*scale, right=shift)
