On Multivariate Discrete Poisson–Lindley Distributions

Multivariate versions of five univariate Poisson–Lindley distributions are considered. These models are derived by assuming that the exponent of a multinomial distribution is a random variable distributed as a Poisson–Lindley. Characteristic properties of all models are given including probabilities various conditional probabilities, and their recurrences, moments and regression functions. It is worth noting that all multivariate characteristics are simple functions of the corresponding properties of the generalizing univariate Poisson–Lindley distribution. In addition, since the multinomial parameters can be estimated by ratios of the marginal means, only the parameters of the univariate Poisson–Lindley model need to be estimated by other estimation methods. An illustrative example is given using automobile insurance claims data.