Noncentral Chi Distribution - Properties

Properties

The probability density function is

f(x;k,\lambda)=\frac{e^{-(x^2+\lambda^2)/2}x^k\lambda} {(\lambda x)^{k/2}} I_{k/2-1}(\lambda x)

where is a modified Bessel function of the first kind.

The first few raw moments are:

where is the generalized Laguerre polynomial. Note that the 2nth moment is the same as the nth moment of the noncentral chi-squared distribution with being replaced by .

Read more about this topic:  Noncentral Chi Distribution

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