"""Nakagami-m distribution."""
import numpy
from scipy import special
from ..baseclass import Dist
from ..operators.addition import Add
class nakagami(Dist):
"""Nakagami-m distribution."""
def __init__(self, nu):
Dist.__init__(self, 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.
class Nakagami(Add):
"""
Nakagami-m distribution.
Args:
shape (float, Dist):
Shape parameter
scale (float, Dist):
Scaling parameter
shift (float, Dist):
Location parameter
Examples:
>>> distribution = chaospy.Nakagami(2, 2, 2)
>>> distribution
Nakagami(scale=2, shape=2, shift=2)
>>> q = numpy.linspace(0,1,6)[1:-1]
>>> distribution.inv(q).round(4)
array([3.284 , 3.6592, 4.0111, 4.4472])
>>> distribution.fwd(distribution.inv(q)).round(4)
array([0.2, 0.4, 0.6, 0.8])
>>> distribution.pdf(distribution.inv(q)).round(4)
array([0.4642, 0.5766, 0.5383, 0.3669])
>>> distribution.sample(4).round(4)
array([4.1137, 3.076 , 5.0824, 3.8012])
>>> distribution.mom(1).round(4)
3.88
"""
def __init__(self, shape=1, scale=1, shift=0):
self._repr = {"shape": shape, "scale": scale, "shift": shift}
Add.__init__(self, nakagami(shape)*scale, shift)
