On the Bivariate Skellam Distribution

Jan Bulla, Christophe Chesneau and Maher Kachour

Communications in Statistics - Theory and Methods, 2015, vol. 44, issue 21, 4552-4567

Abstract: In this article, we introduce a new distribution on Z2$\mathbb {Z}^2$, which can be viewed as a natural bivariate extension of the Skellam distribution. The main feature of this distribution a possible dependence of the univariate components, both following univariate Skellam distributions. We explore various properties of the distribution and investigate the estimation of the unknown parameters via the method of moments and maximum likelihood. In the experimental section, we illustrate our theory. First, we compare the performance of the estimators by means of a simulation study. In the second part, we present two applications to a real data set and show how an improved fit can be achieved by estimating mixture distributions.

Date: 2015
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DOI: 10.1080/03610926.2013.837925

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