Abstract
We propose a definition of a multivariate Linnik distribution based upon closure under geometric compounding. The characteristic function of the multivariate Linnik model is 1/(1 + (∑ m i = 1 s 'Ω i s ) α/2, where 0 < α ⩽ 2, the Ω i 's are r × r positive semi definite matrices and no two of Ω i 's are proportional. The specific case of α = 2 yields a multivariate LaPlace distribution. Estimation methods analogous to those used in estimating the parameters of the stable distribution are presented.
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