Abstract
We define a multivariate gamma distribution on Rn by its Laplace transform (P(-θ))-λ, λ>0, where
P(θ)=∑T⊂{1,…,n}pT∏i∈Tθi.
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
Philippe Bernardoff. "Which multivariate gamma distributions are infinitely divisible?." Bernoulli 12 (1) 169 - 189, February 2006.
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