Afrika Statistika

Comparison between two bivariate Poisson distributions through the phi-divergence

Prévot C. Batsindila Nganga, Rufin Bidounga, Dominique Mizère, and Célestin C. Kokonendji

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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 $\phi$-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.


Dans la littérature, il y a deux modèles probabilistes de Poisson bivariés: le modèle selon Holgate puis le modèle selon Berkhout et Plug. Ces deux modèles sont définis par leur fonction de masse. Le modèle de Holgate met en évidence une corrélation strictement positive, ce qui n'est pas toujours réaliste. Pour remédier à ce problème, Berkhout et Plug ont proposé une distribution de Poisson bivariée acceptant la corrélation aussi bien négative, nulle que positive. Dans ce papier, nous montrons que ces modèles sont presque partout asymptotiquement égaux car la $\phi$-divergence de ces deux modèles converge vers zéro. Aussi, le modèle de Holgate converge vers celui de Berkhout et Plug. Les graphes seront présentés pour illustrer cette comparaison.

Article information

Afr. Stat., Volume 12, Number 3 (2017), 1481-1494.

Received: 29 October 2017
Accepted: 25 November 2017
First available in Project Euclid: 4 January 2018

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G20: Asymptotic properties G2H10 40A05: Convergence and divergence of series and sequences

correlation structure distribution convergence


Nganga, Prévot C. Batsindila; Bidounga, Rufin; Mizère, Dominique; Kokonendji, Célestin C. Comparison between two bivariate Poisson distributions through the phi-divergence. Afr. Stat. 12 (2017), no. 3, 1481--1494. doi:10.16929/as/1481.114.

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