On Stochastic Representations of the Zero–One-Inflated Poisson Lindley Distribution

Abstract

A zero–one-inflated Poisson Lindley distribution has been introduced recently as an alternative to the zero–one-inflated Poisson distribution for describing count data with a substantial number of zeros and ones. Several stochastic representations of the zero–one-inflated Poisson Lindley distribution and their equivalence to some well-known distributions under some conditions are presented. Using these stochastic representations, the distributional properties such as the nth moments, as well as the conditional distributions are discussed. These stochastic representations can be used to explain the relationship between two or more distributions. Several likelihood ratio tests are developed and examined for the presence of one-inflation and fixed rate parameters. The likelihood ratio tests are found to be powerful and have ability to control the error rates as the sample size increases. A sample size of 1000 is acceptable and sufficient for the likelihood ratio tests to be useful.