"""Nakagami-m distribution."""
import numpy
from scipy import special
from ..baseclass import SimpleDistribution, ShiftScaleDistribution
class nakagami(SimpleDistribution):
"""Nakagami-m distribution."""
def __init__(self, nu):
super(nakagami, self).__init__(dict(nu=nu))
def _pdf(self, x, nu):
return (
2
* nu**nu
/ special.gamma(nu)
* (x ** (2 * nu - 1.0))
* numpy.exp(-nu * x * x)
)
def _cdf(self, x, nu):
return special.gammainc(nu, nu * x * x)
def _ppf(self, q, nu):
return numpy.sqrt(1.0 / nu * special.gammaincinv(nu, q))
def _lower(self, nu):
return 0.0
def _upper(self, nu):
return numpy.sqrt(1.0 / nu * special.gammaincinv(nu, 1 - 1e-16))
[docs]class Nakagami(ShiftScaleDistribution):
"""
Nakagami-m distribution.
Args:
shape (float, Distribution):
Shape parameter
scale (float, Distribution):
Scaling parameter
shift (float, Distribution):
Location parameter
Examples:
>>> distribution = chaospy.Nakagami(1.5)
>>> distribution
Nakagami(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. , 0.579, 0.789, 0.991, 1.244, 5.079])
>>> numpy.allclose(distribution.fwd(xloc), uloc)
True
>>> distribution.pdf(xloc).round(3)
array([0. , 0.84 , 1.015, 0.933, 0.63 , 0. ])
>>> distribution.sample(4).round(3)
array([1.05 , 0.465, 1.615, 0.87 ])
"""
[docs] def __init__(self, shape=1, scale=1, shift=0):
super(Nakagami, self).__init__(
dist=nakagami(shape),
scale=scale,
shift=shift,
repr_args=[shape],
)