"""Double gamma distribution."""
import numpy
from scipy import special
from ..baseclass import SimpleDistribution, ShiftScaleDistribution
class double_gamma(SimpleDistribution):
"""Double gamma distribution."""
def __init__(self, a):
super(double_gamma, self).__init__(dict(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))
out = numpy.where(q > 0.5, fac, -fac)
return out
def _lower(self, a):
return -special.gammainccinv(a, 2e-15)
def _upper(self, a):
return special.gammainccinv(a, 2e-15)
[docs]class DoubleGamma(ShiftScaleDistribution):
"""
Double gamma distribution.
Args:
shape (float, Distribution):
Shape parameter
scale (float, Distribution):
Scaling parameter
shift (float, Distribution):
Location parameter
Examples:
>>> distribution = chaospy.DoubleGamma(shape=1.5)
>>> distribution
DoubleGamma(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([-35.769, -1.473, -0.503, 0.503, 1.473, 35.769])
>>> numpy.allclose(distribution.fwd(xloc), uloc)
True
>>> distribution.pdf(xloc).round(3)
array([0. , 0.157, 0.242, 0.242, 0.157, 0. ])
>>> distribution.sample(4).round(3)
array([ 0.727, -2.154, 3.132, -0.138])
"""
[docs] def __init__(self, shape=1, scale=1, shift=0):
super(DoubleGamma, self).__init__(
dist=double_gamma(shape),
scale=scale,
shift=shift,
repr_args=[shape],
)