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# crv_types.Kumaraswamy

All Samples(1)  |  Call(0)  |  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
==========

..  http://en.wikipedia.org/wiki/Kumaraswamy_distribution
"""

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