"""Gamma distribution."""
import numpy
from scipy import special
from ..baseclass import Dist
from ..operators.addition import Add
class gamma(Dist):
def __init__(self, a=1):
Dist.__init__(self, a=a)
def _pdf(self, x, a):
return x**(a-1)*numpy.e**(-x) / special.gamma(a)
def _cdf(self, x, a):
return special.gammainc(a, x)
def _ppf(self, q, a):
return special.gammaincinv(a, q)
def _mom(self, k, a):
return special.gamma(a+k)/special.gamma(a)
def _ttr(self, n, a):
return 2.*n+a, n*n+n*(a-1)
def _lower(self, a):
return 0.
def _upper(self, a):
return 40+2*a
class Gamma(Add):
"""
Gamma distribution.
Also an Erlang distribution when shape=k and scale=1./lamb.
Args:
shape (float, Dist):
Shape parameter. a>0.
scale (float, Dist):
Scale parameter. scale!=0
shift (float, Dist):
Location of the lower bound.
Examples:
>>> distribution = chaospy.Gamma(1, 1, 1)
>>> distribution
Gamma(scale=1, shape=1, shift=1)
>>> q = numpy.linspace(0,1,6)[1:-1]
>>> distribution.inv(q).round(4)
array([1.2231, 1.5108, 1.9163, 2.6094])
>>> distribution.fwd(distribution.inv(q)).round(4)
array([0.2, 0.4, 0.6, 0.8])
>>> distribution.pdf(distribution.inv(q)).round(4)
array([0.8, 0.6, 0.4, 0.2])
>>> distribution.sample(4).round(4)
array([2.0601, 1.1222, 4.0014, 1.6581])
>>> distribution.mom(1)
array(2.)
>>> distribution.ttr([1, 2, 3]).round(4)
array([[4., 6., 8.],
[1., 4., 9.]])
"""
def __init__(self, shape=1, scale=1, shift=0):
self._repr = {"shape": shape, "scale": scale, "shift": shift}
Add.__init__(self, left=gamma(shape)*scale, right=shift)
class Exponential(Add):
R"""
Exponential Probability Distribution
Args:
scale (float, Dist):
Scale parameter. scale!=0
shift (float, Dist):
Location of the lower bound.
Examples;:
>>> distribution = chaospy.Exponential(2, 3)
>>> distribution
Exponential(scale=2, shift=3)
>>> q = numpy.linspace(0,1,6)[1:-1]
>>> distribution.inv(q).round(4)
array([3.4463, 4.0217, 4.8326, 6.2189])
>>> distribution.fwd(distribution.inv(q)).round(4)
array([0.2, 0.4, 0.6, 0.8])
>>> distribution.sample(4).round(4)
array([5.1203, 3.2444, 9.0028, 4.3163])
>>> distribution.mom(1).round(4)
5.0
>>> distribution.ttr([1, 2, 3]).round(4)
array([[ 9., 13., 17.],
[ 4., 16., 36.]])
"""
def __init__(self, scale=1, shift=0):
self._repr = {"scale": scale, "shift": shift}
Add.__init__(self, left=gamma(1)*scale, right=shift)
