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A multivariate Linnik distribution. (English) Zbl 0754.60022

Summary: We propose a definition of a multivariate Linnik distribution based upon closure under geometric compounding. The characteristic function of the multivariate Linnik model is \(1/(1+(\sum^ m_{i=1}s'\Omega_ i s)^{\alpha/2})\), where \(0<\alpha\leq 2\), the \(\Omega_ i\)’s are \(r\times r\) 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.

MSC:

60E05 Probability distributions: general theory
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References:

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