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sympy.stats.Nakagami

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Create a continuous random variable with a Nakagami distribution.

The density of the Nakagami distribution is given by

.. math::
f(x) := \frac{2\mu^\mu}{\Gamma(\mu)\omega^\mu} x^{2\mu-1}
\exp\left(-\frac{\mu}{\omega}x^2 \right)

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


        def Nakagami(name, mu, omega):
r"""
Create a continuous random variable with a Nakagami distribution.

The density of the Nakagami distribution is given by

.. math::
f(x) := \frac{2\mu^\mu}{\Gamma(\mu)\omega^\mu} x^{2\mu-1}
\exp\left(-\frac{\mu}{\omega}x^2 \right)

with :math:x > 0.

Parameters
==========

mu : Real number, \mu \geq \frac{1}{2} a shape
omega : Real number, \omega > 0, the spread

Returns
=======

A RandomSymbol.

Examples
========

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

>>> mu = Symbol("mu", positive=True)
>>> omega = Symbol("omega", positive=True)
>>> z = Symbol("z")

>>> X = Nakagami("x", mu, omega)

>>> D = density(X)(z)
>>> pprint(D, use_unicode=False)
2
-mu*z
-------
mu      -mu  2*mu - 1  omega
2*mu  *omega   *z        *e
----------------------------------
gamma(mu)

>>> simplify(E(X, meijerg=True))
sqrt(mu)*sqrt(omega)*gamma(mu + 1/2)/gamma(mu + 1)

>>> V = simplify(variance(X, meijerg=True))
>>> pprint(V, use_unicode=False)
2
omega*gamma (mu + 1/2)
omega - -----------------------
gamma(mu)*gamma(mu + 1)

References
==========

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

return rv(name, NakagamiDistribution, (mu, omega))


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_nakagami():
mu = Symbol("mu", positive=True)
omega = Symbol("omega", positive=True)

X = Nakagami('x', mu, omega)
assert density(X)(x) == (2*x**(2*mu - 1)*mu**mu*omega**(-mu)
*exp(-x**2*mu/omega)/gamma(mu))
assert simplify(E(X, meijerg=True)) == (sqrt(mu)*sqrt(omega)
*gamma(mu + S.Half)/gamma(mu + 1))
assert simplify(variance(X, meijerg=True)) == (