Geometric-zero truncated poisson distribution: Properties and applications

In this paper, a new discrete distribution is introduced by compounding the geometric distribution with a zero truncated Poisson distribution, named geometric-zero truncated Poisson (GZTP) distribution. Some basic properties of the new distribution, such as the hazard rate function, moments, mode, median, etc., are studied. We show mathematically and numerically that the hazard rate function is increasing. The model parameters are estimated by the moment, least squared error and maximum likelihood methods. A simulation study is performed to compare the performance of the different estimators in terms of bias and mean squared error. An application of the new model is also illustrated using the three real data sets.