On a Class of Bivariate Mixed Sarmanov Distributions

Abstract

In this paper, we extend the class of bivariate Sarmanov distributions by introducing some bivariate mixed Sarmanov distributions. Special attention is paid to the bivariate mixed Sarmanov distribution with Poisson marginals and, in particular, to the resulting bivariate Sarmanov distribution with negative binomial and Poisson-Inverse Gaussian marginals; these particular types of mixed distributions have possible applications in modelling bivariate count data. The extension to higher dimensions is also discussed. Moreover, since one of the purposes of mixing is to obtain new dependency structures, we also present some correlation formulas.

Keywords: Mixed Sarmanov distributions, Correlation coefficient, Poisson marginal distribution, Negative Binomial marginal distribution, Poisson-Inverse Gaussian marginal distribution

JEL Classification: C02, G22, C25