"""Alpha probability distribution."""
import numpy
from scipy import special
import chaospy
from ..baseclass import SimpleDistribution, ShiftScaleDistribution
class alpha(SimpleDistribution):
"""Standard Alpha distribution."""
def __init__(self, a=1):
super(alpha, self).__init__(dict(a=a))
def _cdf(self, x, a):
return special.ndtr(a - 1.0 / x) / special.ndtr(a)
def _ppf(self, q, a):
out = 1.0 / (a - special.ndtri(q * special.ndtr(a)))
return numpy.where(q == 1, self._upper(a), out)
def _pdf(self, x, a):
return numpy.where(
x == 0,
0,
numpy.e ** (-0.5 * (a - 1.0 / x) ** 2)
/ (numpy.sqrt(2 * numpy.pi) * x**2 * special.ndtr(a)),
)
def _lower(self, a):
return 0.0
def _upper(self, a):
return 1.0 / (a - special.ndtri((1 - 1e-10) * special.ndtr(a)))
[docs]class Alpha(ShiftScaleDistribution):
"""
Alpha distribution.
Args:
shape (float, Distribution):
Shape parameter
scale (float, Distribution):
Scale Parameter
shift (float, Distribution):
Location of lower threshold
Examples:
>>> distribution = chaospy.Alpha(6)
>>> distribution
Alpha(6)
>>> 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. , 0.146, 0.16 , 0.174, 0.194, 63.709])
>>> numpy.allclose(distribution.fwd(xloc), uloc)
True
>>> distribution.pdf(xloc).round(3)
array([ 0. , 13.104, 15.108, 12.759, 7.449, 0. ])
>>> distribution.sample(4).round(3)
array([0.178, 0.139, 0.23 , 0.165])
"""
[docs] def __init__(self, shape=1, scale=1, shift=0):
super(Alpha, self).__init__(
dist=alpha(shape),
scale=scale,
shift=shift,
repr_args=[shape],
)