Multivariate discrete exponential family of distributions and their properties

Abstract

The paper generalizes the univariate discrete exponential family of distributions to the multivariate situation, and this generalization includes the multivariate power series distributions, the multivariate Lagrangian distributions, and the modified multivariate power-series distributions. This provides a unified approach for the study of these three classes of distributions. We obtain recurrence relations for moments and cumulants, and the maximum likelihood estimation for the discrete exponential family. These results are applied to some multivariate discrete distributions like the Lagrangian Poisson, Lagrangian (negative) multinomial, logarithmic series distributions and multivariate Lagrangian negative binomial distribution.

Keywords:

• Power series distribution
• Lagrangiandistributions
• Lagrangian (negative) multinomial
• logarithmic series distributions
• maximum likelihood estimates
• moments and cumulants