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# sympy.stats.ChiNoncentral

All Samples(2)  |  Call(1)  |  Derive(0)  |  Import(1)
Create a continuous random variable with a non-central Chi distribution.

The density of the non-central Chi distribution is given by

.. math::
f(x) := \frac{e^{-(x^2+\lambda^2)/2} x^k\lambda}
{(\lambda x)^{k/2}} I_{k/2-1}(\lambda x)

with x \geq 0. Here, I_\nu (x) is the
:ref:modified Bessel function of the first kind <besseli>.(more...)


        def ChiNoncentral(name, k, l):
r"""
Create a continuous random variable with a non-central Chi distribution.

The density of the non-central Chi distribution is given by

.. math::
f(x) := \frac{e^{-(x^2+\lambda^2)/2} x^k\lambda}
{(\lambda x)^{k/2}} I_{k/2-1}(\lambda x)

with x \geq 0. Here, I_\nu (x) is the
:ref:modified Bessel function of the first kind .

Parameters
==========

k : A positive Integer, k > 0, the number of degrees of freedom
l : Shift parameter

Returns
=======

A RandomSymbol.

Examples
========

>>> from sympy.stats import ChiNoncentral, density, E, std
>>> from sympy import Symbol, simplify

>>> k = Symbol("k", integer=True)
>>> l = Symbol("l")
>>> z = Symbol("z")

>>> X = ChiNoncentral("x", k, l)

>>> density(X)(z)
l*z**k*(l*z)**(-k/2)*exp(-l**2/2 - z**2/2)*besseli(k/2 - 1, l*z)

References
==========

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

return rv(name, ChiNoncentralDistribution, (k, l))


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_chi_noncentral():
k = Symbol("k", integer=True)
l = Symbol("l")

X = ChiNoncentral("x", k, l)