On some aspects of a zero-inflated overdispersed model and its applications.

Count data with excess zeros are so common in several areas of scientific research. In particular, the zero-inflated version of count data models has been used for modelling data sets with excessive number of zeros. In this regard, zero-inflated Poisson distribution has received much attention in the literature. Through this paper, we propose a generalized class of zero-inflated Poisson distribution namely 'zero-inflated Hermite distribution (ZIHD)', which can be considered as a more flexible class of zero-inflated Poisson-type distribution suitable for tackling overdispersed data sets. Here we investigate several important properties of the ZIHD along with a discussion on certain inference aspects of the model. Certain test procedures for checking zero-inflation have also been developed and these tests have been investigated by using simulation studies. Further, two real life data applications are given for illustrating the usefulness of the model.