Bivariate doubly inflated Poisson models with applications

Abstract

ABSTRACTThe bivariate Poisson distribution given by Kocherlakota and Kocherlakota is a natural choice for modeling paired count data. For situations where counts of (0, 0) are inflated beyond expectation, the proposed zero-inflated bivariate Poisson distribution by Lee et al. is appropriate. In this article we introduce a bivariate distribution that accounts for inflated counts in both the (0, 0) and (k, k) cells for some k > 0. This bivariate doubly inflated Poisson distribution (BDIP) is a parametric model determined by four or five parameters. We discuss distributional properties of the BDIP model such as identifiability, moments, conditional distributions, and stochastic representations, and provide two methods for parameter estimation. We illustrate model and estimator performance via large sample efficiency comparisons, small sample mean square error estimation, and application in a real-life data set.