The work undertaken by Bidounga et al. [1] highlighted a family of bivariate Poisson distributions. Its elements are weighted bivariate Poisson distributions having for basic function, the bivariate Poisson distributions according to Berkhout and Plug [2]. Some are: the distribution of Poisson bivariate according to Holgate [6], the bivariate Poisson distribution according to Lakshminarayana et al. [7], the bivariate generalized Poisson distribution of Famoye [5], and the bivariate weighted Poisson distribution according to Elion et al. [4]. In this paper, we built a new family of bivariate distributions using the formula of the probabilities of the causes. These are the products of the marginal distributions. With this bivariate distribution are associated several generalized linear models of which the resolution makes it possible to highlight, not only independence between the variables, but also the effect of the factors on these variables. The two families of bivariate distributions have a joint element: the distribution of Poisson bivariate according to Berkhout and Plug [2] considered by Bidounga et al. [1] as a standard distribution in

probability of causes, bivariate Poisson distribution, convex combination, log likelihood, maxLik package.

Received: January 8, 2021; Accepted: January 15, 2021; Published: February 8, 2021

How to cite this article: Rufin Bidounga, E. G. Brunel Mandangui Maloumbi, Réolie Foxie Mizélé Kitoti, P. C. Batsindila Nganga and  Dominique Mizère, Construction of a family of bivariate distributions using the probabilities of causes, Far East Journal of Theoretical Statistics 61(1) (2021), 35-48. DOI: 10.17654/TS061010035

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:

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