Kokonendji, Célestin Clotaire 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 C. R. Acad. Sci., Paris, Sér. I 314, No. 13, 1063-1068 (1992). 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. Cited in 4 Documents MSC: 62E10 Characterization and structure theory of statistical distributions Keywords:Mora class; Laplace transform; characterization; natural exponential families; Seshadri’s variance functions; strictly cubic polynomial; affine function of the mean PDFBibTeX XMLCite \textit{C. C. Kokonendji}, C. R. Acad. Sci., Paris, Sér. I 314, No. 13, 1063--1068 (1992; Zbl 0755.62022)