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Positive Dependence of the Bivariate and Trivariate Absolute Normal, $t, \chi^2$ , and $F$ DistributionsPositive Dependence of the Bivariate and Trivariate Absolute Normal, $t, \chi^2$, and $F$ Distributions

M. Abdel-Hameed · Allan R. Sampson刊期 1978-11-01 · 卷 6（6）The Annals of Statistics已编入正刊

二元与三元绝对正态、t、卡方及 F 分布的正相依性AI 解读

It is shown that the bivariate density of the absolute normal distribution is totally positive of order 2. Necessary and sufficient conditions are given for the trivariate density of the absolute normal distribution to be totally positive of order 2 in pairs of arguments. These results are then used to show that certain generalized bivariate and trivariate $t, \chi^2$ and $F$ random variables are associated.It is shown that the bivariate density of the absolute normal distribution is totally positive of order 2. Necessary and sufficient conditions are given for the trivariate density of the absolute normal distribution to be totally positive of order 2 in pairs of arguments. These results are then used to show that certain generalized bivariate and trivariate $t, \chi^2$ and $F$ random variables are associated.

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被引 26 次 ↗OpenAlex · 核验 2026-10-04

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Positive Dependence of the Bivariate and Trivariate Absolute Normal, t,χ2t, \chi^2t,χ2, and FFF DistributionsPositive Dependence of the Bivariate and Trivariate Absolute Normal, $t, \chi^2$, and $F$ Distributions

Positive Dependence of the Bivariate and Trivariate Absolute Normal, $t, \chi^2$ , and $F$ DistributionsPositive Dependence of the Bivariate and Trivariate Absolute Normal, $t, \chi^2$, and $F$ Distributions