Bivariate natural exponential families with linear diagonal variance functions

• Autorzy: Chachulska J.
• Języki publikacji: EN

Abstrakty

EN

It is well known that natural exponential families (NEFs) are uniquely determined by their variance functions (VFs). However, there exist examples showing that even an incomplete knowledge of a matrix VF can be sufficient to determine a multivariate NEF. Following such an idea, in this paper a complete description of bivariate NEFs with linear diagonal of the matrix VF is given. As a result we obtain the families of distributions with marginals that are some combinations of Poisson and normal distributions. Furthermore, the characterization extends (in two-dimensional case) the classification of NEFs with linear matrix VF obtained by Letac [11]. The main result is formulated in terms of regression properties.

Słowa kluczowe

EN

natural exponential families; variance function; Laplace transforms

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2010
• Tom: Vol. 30, Fasc. 1
• Strony: 121--139
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Chachulska J.

• Faculty of Mathematics and Information Science, Warsaw University of Technology, 00-661 Warsaw, Poland

Bibliografia

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