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February 2006 Which multivariate gamma distributions are infinitely divisible?
Philippe Bernardoff
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Bernoulli 12(1): 169-189 (February 2006).

Abstract

We define a multivariate gamma distribution on Rn by its Laplace transform (P(-θ))-λ, λ>0, where

P(θ)=T{1,,n}pTiTθi.

Under p{1,,n}0, we establish necessary and sufficient conditions on the coefficients of P, such that the above function is the Laplace transform of some probability distribution, for all λ>0, thus characterizing all infinitely divisible multivariate gamma distributions on Rn.

Citation

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Philippe Bernardoff. "Which multivariate gamma distributions are infinitely divisible?." Bernoulli 12 (1) 169 - 189, February 2006.

Information

Published: February 2006
First available in Project Euclid: 28 February 2006

zbMATH: 1101.60008
MathSciNet: MR2202328

Keywords: Bell polynomials , exponential families , Frullani integral , generalized hypergeometric series , infinitely divisible distribution , Laplace transform , multivariate gamma distribution , Stirling numbers of the second kind

Rights: Copyright © 2006 Bernoulli Society for Mathematical Statistics and Probability

Vol.12 • No. 1 • February 2006
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