Comparison between two bivariate Poisson distributions through the phi-divergence

Abstract

Abstract. In the literature, there are two probabilistic models of bivariate Poisson : the model according to Holgate and the model according to Berkhout and Plug. These two models express themselves by their probability mass function. The model of Holgate puts in evidence a strictly positive correlation, which is not always realistic. To remedy this problem, Berkhout and Plug proposed a bivariate Poisson distribution accepting the correlation as well negative, equal to zero, that positive. In this paper, we show that these models are nearly everywhere asymptotically equal. From this survey that the φ-divergence converges toward zero, both models are therefore nearly everywhere equal. Also, the model of Holgate converges toward the one of Berkhout and Plug. Some graphs will be presented for illustrating this comparison.

Editorial to the fourth issue of Afrika Statistika devoted to probability laws, to their statistical properties and to their characterizations each year

“…We already published a sample of alike papers : Okorie et al (2017), Radakumari and Irshad (2017), Nganga et al (2017), Tour and Yahia (2017), Gyan (2017), Elbatal et al (2016) and Zeghdoudi and Nedjar (2016), in Afrika Statistika, in 2016 and 2017. From now, papers of that type will be published in the last issue of the year.…”