engleski

CDF of non-central χ^2 distribution revisited. Incomplete hypergeometric type functions approach

The cumulative distribution function of the non-central chi-square distribution χ′2 ν (λ), ν ∈ R+ possesses an integral representation in terms of a generalized Marcum Q-function. Regarding some already known-results, here we derive a simpler form of the cumulative distribution function for ν = 2n ∈ N degrees of freedom. Also, we express these representations in terms of an incomplete Fox–Wright function pΨ γ )q and the generalized incomplete hypergeometric functions concerning the important special cases such as 1Γ1, 2Γ1 and 2γ1. New identities are established between 1Γ1 and 2Γ1 as well.

CDF of non-central χ^2 distribution ; Modified Bessel function of the first kind ; Marcum Q-function ; Incomplete gamma function ; (In)complete Fox-Wright function ; Generalized (in)complete hypergeometric functions.

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