One-Inflated Zero-Truncated Poisson Distribution: Statistical Properties and Real Life Applications

Agriculture, engineering, public health, sociology, psychology, and epidemiology are just few of the numerous disciplines that find analysis and modeling of zero-truncated count data to be of paramount importance. Very recently, researchers have been paying careful attention to the one-inflation implications of these zero-truncated count statistics. In this regard, we have studied the one-inflated variant of the zero-truncated Poisson distribution. There are few models within the proposed distribution, which itself is a representation of a two-part process. We have calculated crucial statistical characteristics of the suggested model which are not confined to generating functions, moments and associated measures. The parametric estimation has been carried out using the maximum likelihood estimation. Two different simulation studies have been carried out, one to test the performance of maximum likelihood estimates and the other for testing the compatibility of our devised model when data has been simulated from different competing models with considerably higher mass at point one. For the purpose of testing the compatibility of our proposed model, we have used three real life data sets and considered theoretical as well as graphical performance measures. The fitting results have been compared with some other models of interest. Moreover, we have used three different test statistics viz. Likelihood ratio test, Wald’s test, and Rao’s efficient score test for the purpose of testing the significance of one-inflation parameter.