On the bivariate Skellam distribution

Jan Bulla (1) , Christophe Chesneau (1) , Maher Kachour (2)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 IDRAC Business school Lyon - Institut pour le Développement et la Recherche d'Action Commerciale

In this paper, we introduce a new distribution on Z2, 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 and an application to a real data set and show how an improved fit can be achieved by estimating mixture distributions.

Mots clés: Maximum likelihood estimate; Skellam distribution; Bivariate Skellam distribution; Maximum likelihood estimate.

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Jan Bulla, Christophe Chesneau, Maher Kachour. On the bivariate Skellam distribution. 2013. ⟨hal-00744355v2⟩