论文标题
重新审视非中央$χ^2 $分配的CDF。不完整的超几何类型函数方法
CDF of non-central $χ^2$ distribution revisited. Incomplete hypergeometric type functions approach
论文作者
论文摘要
非中心卡方分布的累积分布函数$χ_ν'^2（λ），\，c in \ Mathbb {r}^+$在广义Marcum $ q $ function方面具有积分表示。关于一些已经知道的结果，在这里，我们得出了$ν= 2n \ in \ mathbb {n} $自由度的累积分布函数的更简单形式。 Also, we express these representations in terms of an incomplete Fox-Wright function ${}_pΨ_q^{(γ)}$ and the generalized incomplete hypergeometric functions concerning the important special cases as ${}_1Γ_1,\, {}_2Γ_1$ and ${}_2γ_1$. $ {} _1γ_1$和$ {} _2γ_1$之间建立了新的身份。
The cumulative distribution function of the non-central chi-square distribution $χ_ν'^2(λ),\, ν\in\mathbb{R}^+$ 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 $ν= 2n \in\mathbb{N}$ degrees of freedom. Also, we express these representations in terms of an incomplete Fox-Wright function ${}_pΨ_q^{(γ)}$ and the generalized incomplete hypergeometric functions concerning the important special cases as ${}_1Γ_1,\, {}_2Γ_1$ and ${}_2γ_1$. New identities are established between ${}_1Γ_1$ and ${}_2Γ_1$ as well.
