"""Alpha probability distribution."""
import numpy
from scipy import special
from ..baseclass import Dist
from ..operators.addition import Add
class alpha(Dist):
"""Standard Alpha distribution."""
def __init__(self, a=1):
Dist.__init__(self, a=a)
def _cdf(self, x, a):
return special.ndtr(a-1./x) / special.ndtr(a)
def _ppf(self, q, a):
return 1.0/(a-special.ndtri(q*special.ndtr(a)))
def _pdf(self, x, a):
return (1.0/(x**2)/special.ndtr(a)*
numpy.e**(.5*(a-1.0/x)**2)/numpy.sqrt(2*numpy.pi))
def _lower(self, a):
return 0.
class Alpha(Add):
"""
Alpha distribution.
Args:
shape (float, Dist):
Shape parameter
scale (float, Dist):
Scale Parameter
shift (float, Dist):
Location of lower threshold
Examples:
>>> distribution = chaospy.Alpha(2, 0.5, 4)
>>> distribution
Alpha(scale=0.5, shape=2, shift=4)
>>> q = numpy.linspace(0, 1, 7)[1:-1]
>>> distribution.inv(q).round(4)
array([4.1676, 4.2039, 4.2465, 4.3104, 4.4521])
>>> distribution.fwd(distribution.inv(q)).round(4)
array([0.1667, 0.3333, 0.5 , 0.6667, 0.8333])
>>> distribution.pdf(distribution.inv(q)).round(4)
array([11.7723, 5.4345, 3.361 , 2.2848, 1.4892])
>>> distribution.sample(4).round(4)
array([4.304 , 4.1556, 4.9362, 4.2413])
"""
def __init__(self, shape=1, scale=1, shift=0):
self._repr = {"shape": shape, "scale": scale, "shift": shift}
Add.__init__(self, left=alpha(shape)*scale, right=shift)
