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A Characterization of Poisson–Gaussian Families by Convolution-Stability

✍ Scribed by A.E. Koudou; D. Pommeret

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
104 KB
Volume
81
Category
Article
ISSN
0047-259X

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✦ Synopsis

If the convolution of natural exponential families on R d is still a natural exponential family, then the families are all Poisson-Gaussian, up to affinity. This statement is a generalization of the one-dimensional versions proved by G. Letac (1992, ''Lectures on Natural Exponential Functions and Their Variance Functions,'' Instituto de Matema ´tica pura e aplicada: Monografias de matema ´tica, 50, Rı ´o de Janeiro) in the case of two families, and by D. Pommeret (1999, C. R. Acad. Sci. Ser. I 328, 929-933) for more than two families.

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