"""Log-gamma distribution."""
import numpy
from scipy import special
from ..baseclass import SimpleDistribution, ShiftScaleDistribution
class log_gamma(SimpleDistribution):
"""Log-gamma distribution."""
def __init__(self, c):
super(log_gamma, self).__init__(dict(c=c))
def _pdf(self, x, c):
return numpy.exp(c * x - numpy.exp(x) - special.gammaln(c))
def _cdf(self, x, c):
return special.gammainc(c, numpy.exp(x))
def _ppf(self, q, c):
return numpy.log(special.gammaincinv(c, q))
def _lower(self, c):
return numpy.log(special.gammaincinv(c, 1e-15))
def _upper(self, c):
return numpy.log(special.gammaincinv(c, 1 - 1e-15))
[docs]class LogGamma(ShiftScaleDistribution):
"""
Log-gamma distribution
Args:
shape (float, Distribution):
Shape parameter
scale (float, Distribution):
Scaling parameter
shift (float, Distribution):
Location parameter
Examples:
>>> distribution = chaospy.LogGamma(1.5)
>>> distribution
LogGamma(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([-22.836, -0.688, -0.068, 0.387, 0.842, 3.597])
>>> numpy.allclose(distribution.fwd(xloc), uloc)
True
>>> distribution.pdf(xloc).round(3)
array([0. , 0.243, 0.4 , 0.462, 0.392, 0. ])
>>> distribution.sample(4).round(3)
array([ 0.503, -1.125, 1.364, 0.128])
"""
[docs] def __init__(self, shape=1, scale=1, shift=0):
super(LogGamma, self).__init__(
dist=log_gamma(shape),
scale=scale,
shift=shift,
repr_args=[shape],
)