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# sympy.stats.GammaInverse

All Samples(2)  |  Call(1)  |  Derive(0)  |  Import(1)
Create a continuous random variable with an inverse Gamma distribution.

The density of the inverse Gamma distribution is given by

.. math::
f(x) := \frac{\beta^\alpha}{\Gamma(\alpha)} x^{-\alpha - 1}
\exp\left(\frac{-\beta}{x}\right)

with :math:x > 0.
(more...)


        def GammaInverse(name, a, b):
r"""
Create a continuous random variable with an inverse Gamma distribution.

The density of the inverse Gamma distribution is given by

.. math::
f(x) := \frac{\beta^\alpha}{\Gamma(\alpha)} x^{-\alpha - 1}
\exp\left(\frac{-\beta}{x}\right)

with :math:x > 0.

Parameters
==========

a : Real number, a > 0 a shape
b : Real number, b > 0 a scale

Returns
=======

A RandomSymbol.

Examples
========

>>> from sympy.stats import GammaInverse, density, cdf, E, variance
>>> from sympy import Symbol, pprint

>>> a = Symbol("a", positive=True)
>>> b = Symbol("b", positive=True)
>>> z = Symbol("z")

>>> X = GammaInverse("x", a, b)

>>> D = density(X)(z)
>>> pprint(D, use_unicode=False)
-b
---
a  -a - 1   z
b *z      *e
---------------
gamma(a)

References
==========

.. [1] http://en.wikipedia.org/wiki/Inverse-gamma_distribution
"""

return rv(name, GammaInverseDistribution, (a, b))


from sympy.stats import (P, E, where, density, variance, covariance, skewness,
given, pspace, cdf, ContinuousRV, sample,
Arcsin, Benini, Beta, BetaPrime, Cauchy,
Chi, ChiSquared,
ChiNoncentral, Dagum, Erlang, Exponential,

def test_gamma_inverse():
a = Symbol("a", positive=True)
b = Symbol("b", positive=True)

X = GammaInverse("x", a, b)