On the Bivariate Skellam Distribution

Abstract

In this article, we introduce a new distribution on , 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.

Keywords.:

• Skellam distribution
• Bivariate Skellam distribution
• Maximum likelihood estimate.

Mathematics Subject Classification:

• 62G30
• 62E10.