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On Infinitely Divisible Exponential Dispersion Model Related to Poisson-Exponential Distribution |
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| Authors: | Vladimir Vinogradov |
| Institution: | 1. Department of Mathematics , Ohio University , Athens, Ohio, USA vlavin@math.ohiou.edu |
| Abstract: | We construct a univariate exponential dispersion model comprised of discrete infinitely divisible distributions. This model emerges in the theory of branching processes. We obtain a representation for the Lévy measure of relevant distributions and characterize their laws as Poisson mixtures and/or compound Poisson distributions. The regularity of the unit variance function of this model is employed for the derivation of approximations by the Poisson-exponential model. We emphasize the role of the latter class. We construct local approximations relating them to properties of special functions and branching diffusions. |
| Keywords: | Bessel function Branching process Compound Poisson distribution Confluent hypergeometric function Lévy measure Local approximation Poisson mixture Pólya-Aeppli distribution Power-variance family Rao damage process Tweedie exponential dispersion models Unit variance function Weak convergence |