"""Double gamma distribution."""
import numpy
from scipy import special
from ..baseclass import Dist
from ..operators.addition import Add
class double_gamma(Dist):
"""Double gamma distribution."""
def __init__(self, a):
Dist.__init__(self, a=a)
def _pdf(self, x, a):
ax = abs(x)
return 1.0/(2*special.gamma(a))*ax**(a-1.0) * numpy.exp(-ax)
def _cdf(self, x, a):
fac = 0.5*special.gammainc(a,abs(x))
return numpy.where(x>0,0.5+fac,0.5-fac)
def _ppf(self, q, a):
fac = special.gammainccinv(a,1-abs(2*q-1))
return numpy.where(q>0.5, fac, -fac)
class DoubleGamma(Add):
"""
Double gamma distribution.
Args:
shape (float, Dist):
Shape parameter
scale (float, Dist):
Scaling parameter
shift (float, Dist):
Location parameter
Examples:
>>> distribution = chaospy.DoubleGamma(2, 4, 2)
>>> distribution
DoubleGamma(scale=4, shape=2, shift=2)
>>> q = numpy.linspace(0, 1, 5)
>>> distribution.inv(q).round(4)
array([-100.4566, -4.7134, 2. , 8.7134, 104.4566])
>>> distribution.fwd(distribution.inv(q)).round(4)
array([0. , 0.25, 0.5 , 0.75, 1. ])
>>> distribution.pdf(distribution.inv(q)).round(4)
array([0. , 0.0392, 0. , 0.0392, 0. ])
>>> distribution.sample(4).round(4)
array([ 6.4679, -9.2251, 17.5874, 0.8239])
>>> distribution.mom(1).round(4)
2.0
"""
def __init__(self, shape=1, scale=1, shift=0):
self._repr = {"shape": shape, "scale": scale, "shift": shift}
Add.__init__(self, left=double_gamma(shape)*scale, right=shift)
