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CDF of non-central χ2 distribution revisited. Incomplete hypergeometric type functions approach
Indagationes Mathematicae ( IF 0.5 ) Pub Date : 2021-06-17 , DOI: 10.1016/j.indag.2021.06.005
Dragana Jankov Maširević , Tibor K. Pogány

The cumulative distribution function of the non-central chi-square distribution χν2(λ),νR+ 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=2nN degrees of freedom. Also, we express these representations in terms of an incomplete Fox–Wright function pΨq(γ) 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.



中文翻译:

非中心的 CDF χ2分布重新审视。不完全超几何类型函数方法

非中心卡方分布的累积分布函数 χν2(λ),ν电阻+ 在广义 Marcum 方面具有积分表示 -功能。关于一些已知的结果,这里我们推导出一个更简单的累积分布函数形式ν=2nN自由程度。此外,我们用不完整的 Fox-Wright 函数来表达这些表示Ψq(γ) 以及有关重要特殊情况的广义不完全超几何函数,例如 1Γ1,2Γ12γ1. 之间建立了新的身份1Γ12Γ1 以及。

更新日期:2021-07-09
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