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.
Publié le : 1978-11-14
Classification:
Total positivity,
positive quadrant dependence,
conditionally increasing in sequence,
association,
multivariate $t$ distribution,
multivariate $F$ distribution,
multivariate normal distribution,
62H05
@article{1176344381,
author = {Abdel-Hameed, M. and Sampson, Allan R.},
title = {Positive Dependence of the Bivariate and Trivariate Absolute Normal, $t, \chi^2$, and $F$ Distributions},
journal = {Ann. Statist.},
volume = {6},
number = {1},
year = {1978},
pages = { 1360-1368},
language = {en},
url = {http://dml.mathdoc.fr/item/1176344381}
}
Abdel-Hameed, M.; Sampson, Allan R. Positive Dependence of the Bivariate and Trivariate Absolute Normal, $t, \chi^2$, and $F$ Distributions. Ann. Statist., Tome 6 (1978) no. 1, pp. 1360-1368. http://gdmltest.u-ga.fr/item/1176344381/