- Volume 12, Number 2 (2006), 371-379.
A characterization of Poisson-Gaussian families by generalized variance
We show that if the generalized variance of an infinitely divisible natural exponential family in a -dimensional linear space is of the form , then there exists in such that is a product of univariate Poisson and ()-variate Gaussian families. In proving this fact, we use a suitable representation of the generalized variance as a Laplace transform and the result, due to Jörgens, Calabi and Pogorelov, that any strictly convex smooth function defined on the whole of such that is a positive constant must be a quadratic form.
Bernoulli, Volume 12, Number 2 (2006), 371-379.
First available in Project Euclid: 25 April 2006
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Kokonendji, Célestin C.; Masmoudi, Afif. A characterization of Poisson-Gaussian families by generalized variance. Bernoulli 12 (2006), no. 2, 371--379. doi:10.3150/bj/1145993979. https://projecteuclid.org/euclid.bj/1145993979