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On bivariate distributions with Polya-Aeppli or Lüders-Delaporte marginals. (English) Zbl 0904.62066

Beneš, Viktor (ed.) et al., Distributions with given marginals and moment problems. Proceedings of the 1996 conference, Prague, Czech Republic. Dordrecht: Kluwer Academic Publishers. 93-98 (1997).
This paper presents bivariate discrete distributions that arise as mixtures of particular univariate discrete distributions. Bivariate extensions of some discrete distributions are introduced. In particular, the described distributions have marginal distributions that are either the Polya-Aeppli or the Lüders-Delaporte distributions, respectively. The mechanism for generating these distributions is similar to the one giving rise to the univariate counterparts.
Thus, the bivariate distributions with Polya-Aeppli marginals arise either as a mixture of a bivariate Pascal with a Poisson mixing distribution or as a mixture of two independent Pascal distributions with a bivariate Poisson distribution as the mixing distribution. The bivariate distributions with Lüders-Delaporte marginals are obtained either as a mixed bivariate Poisson distribution with a shifted Gamma mixing distribution or as a mixture of two independent Poisson distributions with a shifted Mardia bivariate Gamma distribution as the mixing distribution. Properties for some of the distributions are briefly described including recurrence relations for the probabilities and the moments as well as the forms of the conditional distributions.
For the entire collection see [Zbl 0885.00054].
Reviewer: D.Karlis

MSC:

62H05 Characterization and structure theory for multivariate probability distributions; copulas
60E05 Probability distributions: general theory
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