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Characterizations of some polynomial variance functions byd-pseudo-orthogonality

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Abstract

From a notion ofd-pseudo-orthogonality for a sequence of polynomials (d ∈ {2,3, …}), this paper introduces three different characterizations of natural exponential families (NEF's) with polynomial variance functions of exact degree 2d-1. These results provide extended versions of the Meixner (1934), Shanbhag (1972), 1979) and Feinsilver (1986) characterization results of quadratic NEF's based on classical orthogonal polynomials. Some news sets of polynomials with (2d-1)-term recurrence relation are then pointed out and we completely illustrate the cases associated to the families of positive stable distributions.

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Authors and Affiliations

  1. Department of Statistics, IUT STID-LMA CNRS, University of Pau, Avenue de l'université, 64000, Pau, France

    Célestin C. Kokonendji

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  1. Célestin C. Kokonendji
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Correspondence to Célestin C. Kokonendji.

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Célestin C. Kokonendji received his Ph. D at Paul Sabatier University of Toulouse (France) under the direction of Gérard Letac. Since 1995 he has always been at the University of Pau. His research interests center on the exponential families in Statistics and Applied Probability. Also, he sometimes does statistical consulting.

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Kokonendji, C.C. Characterizations of some polynomial variance functions byd-pseudo-orthogonality. JAMC 19, 427–438 (2005). https://doi.org/10.1007/BF02935816

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  • DOI: https://doi.org/10.1007/BF02935816

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