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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))
        


src/s/y/sympy-HEAD/sympy/stats/tests/test_continuous_rv.py   sympy(Download)
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)