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November, 1978 Positive Dependence of the Bivariate and Trivariate Absolute Normal, $t, \chi^2$, and $F$ Distributions
M. Abdel-Hameed, Allan R. Sampson
Ann. Statist. 6(6): 1360-1368 (November, 1978). DOI: 10.1214/aos/1176344381

Abstract

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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M. Abdel-Hameed. Allan R. Sampson. "Positive Dependence of the Bivariate and Trivariate Absolute Normal, $t, \chi^2$, and $F$ Distributions." Ann. Statist. 6 (6) 1360 - 1368, November, 1978. https://doi.org/10.1214/aos/1176344381

Information

Published: November, 1978
First available in Project Euclid: 12 April 2007

zbMATH: 0392.62033
MathSciNet: MR523770
Digital Object Identifier: 10.1214/aos/1176344381

Subjects:
Primary: 62H05

Keywords: association , Conditionally increasing in sequence , multivariate $F$ distribution , multivariate $t$ distribution , multivariate normal distribution , positive quadrant dependence , total positivity

Rights: Copyright © 1978 Institute of Mathematical Statistics

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Vol.6 • No. 6 • November, 1978
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