Afrika Statistika

The covariance structure of the bivariate weighted Poisson distribution and application to the Aleurodicus data

Prevot Chirac BATSINDILA NGANGA, Rufin BIDOUNGA, and Dominique MIZÈRE

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Abstract

We meet in the literature the bivariate Poisson distribution put in evidence by Berkhout and Plug. From this distribution, Elion et al. put in evidence the bivariate weighted Poisson distribution like crossing of two univariate weighted Poisson distributions. The structure of the covariance of this bivariate weighted Poisson distribution has been put not again in evidence in the literature. Thus, in this paper, we remedy this hiatus. The overdispersion, underdispersion and the equidispersion will be valued with the help of the Fisher dispersion index for multivariate count distributions introduces by Kokonendji et al. An illustrative example based on the Aleurodicus data is presented.

Résumé

Nous rencontrons dans la littérature la distribution de Poisson bivariée mise en évidence par Berkhout et Plug. De cette distribution, Elion et al. ont mis en évidence la distribution de Poisson pondérée bivariée comme le croisement de deux distributions de Poisson pondérées univariées. La structure de la covariance de cette distribution de Poisson pondérée bivariée n'a pas encore été mise en évidence dans la littérature. Ainsi, dans ce papier, nous remédions à cette lacune. La surdispersion, la sous-dispersion et l'équidispersion seront évaluées à l'aide de l'indice de dispersion de Fisher, pour les distributions de comptage multivariées, introduit par Kokonendji et al. Un exemple illustratif basé sur les données Aleurodicus est présenté.

Article information

Source
Afr. Stat., Volume 14, Number 2 (2019), 1999-2017.

Dates
First available in Project Euclid: 21 August 2019

Permanent link to this document
https://projecteuclid.org/euclid.as/1566353036

Digital Object Identifier
doi:10.16929/as/2019.1999.146

Mathematical Reviews number (MathSciNet)
MR3995013

Zentralblatt MATH identifier
07104737

Subjects
Primary: 62F10: Point estimation
Secondary: 62J12: Generalized linear models

Keywords
bivariate dispersion index moment generating function conditional law

Citation

BATSINDILA NGANGA, Prevot Chirac; BIDOUNGA, Rufin; MIZÈRE, Dominique. The covariance structure of the bivariate weighted Poisson distribution and application to the Aleurodicus data. Afr. Stat. 14 (2019), no. 2, 1999--2017. doi:10.16929/as/2019.1999.146. https://projecteuclid.org/euclid.as/1566353036


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