A multivariate Linnik distribution

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 + ([summation operator]mi = 1s'[Omega]is)[alpha]/2, where 0 < [alpha] [less-than-or-equals, slant] 2, the [Omega]i's are r x r positive semi definite matrices and no two of [Omega]i's are proportional. The specific case of [alpha] = 2 yields a multivariate LaPlace distribution. Estimation methods analogous to those used in estimating the parameters of the stable distribution are presented.