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# sympy.stats.Kumaraswamy

All Samples(2)  |  Call(1)  |  Derive(0)  |  Import(1)
Create a Continuous Random Variable with a Kumaraswamy distribution.

The density of the Kumaraswamy distribution is given by

.. math::
f(x) := a b x^{a-1} (1-x^a)^{b-1}

with :math:x \in [0,1].

Parameters(more...)


        def Kumaraswamy(name, a, b):
r"""
Create a Continuous Random Variable with a Kumaraswamy distribution.

The density of the Kumaraswamy distribution is given by

.. math::
f(x) := a b x^{a-1} (1-x^a)^{b-1}

with :math:x \in [0,1].

Parameters
==========

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

Returns
=======

A RandomSymbol.

Examples
========

>>> from sympy.stats import Kumaraswamy, density, E, variance
>>> from sympy import Symbol, simplify, pprint

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

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

>>> D = density(X)(z)
>>> pprint(D, use_unicode=False)
b - 1
a - 1 /   a    \
a*b*z     *\- z  + 1/

References
==========

.. [1] http://en.wikipedia.org/wiki/Kumaraswamy_distribution
"""

return rv(name, KumaraswamyDistribution, (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_kumaraswamy():
a = Symbol("a", positive=True)
b = Symbol("b", positive=True)

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