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Caractérisation des fonctions variances de Seshadri des familles exponentielles sur \(\mathbb{R}\). (A characterization of Seshadri’s variance functions of exponential families on \(\mathbb{R}\)). (French. Abridged English version) Zbl 0755.62022

Summary: This note characterizes in six types, as for the set \({\mathcal M}_ 3\) of natural exponential families (NEF) with strictly cubic variance functions, the set \({\mathcal S}_ 3\) of NEF with Seshadri’s variance functions \(\sqrt{\Delta}P\) (\(\sqrt{\Delta}\)), where \(P\) is a strictly cubic polynomial and \(\Delta\) is some affine function of the mean.

MSC:

62E10 Characterization and structure theory of statistical distributions
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