Generalized geometric zero-truncated Poisson distribution: Properties and numerical analysis

This article introduces a new discrete probability distribution, namely, the generalized geometric zero-truncated Poisson (GGZTP) distribution which contains two parameters. It is derived by combining geometric and zero-truncated Poisson distributions. The GGZTP distribution offers a more flexible tool for modeling a wider variety of count data due to its advantageous index of dispersion. Several statistical functions of the proposed distribution are derived. Maximum likelihood estimation is employed to find estimators of the GGZTP's parameters. A simulation study is then conducted to examine the performance of the proposed estimator. The results show that the average estimate for each parameter approaches its actual value as the sample size increases.