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Multivariate stable exponential families and Tweedie scale
Authors:A Hassairi  M Louati
Institution:Laboratory of Probability and Statistics, Sfax Faculty of Sciences, B.P. 802, Tunisia
Abstract:In this paper, we characterize the multivariate stable natural exponential families by a property of homogeneity of the cumulant function of some basis, and by a property of homogeneity of the variance function. We also extend the definition of a Tweedie scale to a finite dimensional space and we give a class of natural exponential families belonging to this scale on the space of symmetric matrices.
Keywords:Stable distribution  Natural exponential family  Variance function  Tweedie scale
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