Geodesic
On a Bivariate Katz's Distribution Constructed by the Trivariate Reduction Method
Serdica Journal of Computing, Tome 17 (2023) no. 2, pp. 79-93.

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In this paper, we propose the bivariate distribution of the Katz distribution [1] constructed by the trivariate reduction method, method developed in [6] and used in [5] to give an equivalent definition of the bivariate Poisson distribution [7, 8]. The constructed distribution includes, in particular, the bivariate Poisson distribution [5] and has interesting properties. For the estimation of the parameters, we used two methods: the method of moments and the maximum likelihood method using the EM algorithm. An application to concrete data has been made in order to carry out a comparative study between bivariate Poisson and Katz distributions, and we discuss the likelihood-ratio test, which assesses the goodness of fit of two competing statistical models.
Keywords: bivariate distributions, trivariate reduction method, Katz's distribution, EM algorithm, likelihood ratio test, multivariate count data 
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     title = {On a {Bivariate} {Katz's} {Distribution} {Constructed} by the {Trivariate} {Reduction} {Method}},
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Koukouatikissa Diafouka, Michel; Louzayadio, Chedly Gélin. On a Bivariate Katz's Distribution Constructed by the Trivariate Reduction Method. Serdica Journal of Computing, Tome 17 (2023) no. 2, pp. 79-93. http://geodesic.mathdoc.fr/item/SJC_2023_17_2_a0/