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The bivariate non-central negative binomial distributions. (English) Zbl 0601.62067
The paper introduces four bivariate generalizations of the non-central negative binomial distribution studied earlier by the same authors [Biom. J. 21, 611-627 (1979; Zbl 0432.62011)]. The three of them are constructed using the ”latent structure model” scheme [L. A. Goodman, Biometrika 61, 215-231 (1974; Zbl 0281.62057)] and some variants of it. The other generalization is formed by using the method of random elements in common. The paper provides probabilities recurrence formulae, moments and other properties of these distributions. Finally, an application is considered.
Reviewer: J.Panaretos

MSC:
62H10 Multivariate distribution of statistics
62E10 Characterization and structure theory of statistical distributions
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