We define a multivariate gamma distribution on [math] by its Laplace transform [math] , [math] where ¶
[math]
¶ Under [math] , we establish necessary and sufficient conditions on the coefficients of [math] such that the above function is the Laplace transform of some probability distribution, for all [math] thus characterizing all infinitely divisible multivariate gamma distributions on [math]
Publié le : 2006-02-14
Classification:
Bell polynomials,
exponential families,
Frullani integral,
generalized hypergeometric series,
infinitely divisible distribution,
Laplace transform,
multivariate gamma distribution,
Stirling numbers of the second kind
@article{1141136656,
author = {Bernardoff, Philippe},
title = {Which multivariate gamma distributions are infinitely divisible?},
journal = {Bernoulli},
volume = {12},
number = {2},
year = {2006},
pages = { 169-189},
language = {en},
url = {http://dml.mathdoc.fr/item/1141136656}
}
Bernardoff, Philippe. Which multivariate gamma distributions are infinitely divisible?. Bernoulli, Tome 12 (2006) no. 2, pp. 169-189. http://gdmltest.u-ga.fr/item/1141136656/