A new compounding life distribution: gamma zero-truncated poisson distribution

Modeling of lifetimes is an important statistical work in many fields. This study introduces novel continuous three-parameter lifetime distributions known as the gamma zero-truncated Poisson (GZTP) and complementary gamma zero-truncated Poisson (CGZTP) distributions. These distributions compound minimum or maximum value from a set of independent, identical gamma-distributed random variables, with zero-truncated Poisson random variables. Properties of the proposed distributions, including the probability density, cumulative distribution, survival, and hazard functions as well as moments, are studied and mathematically proven. The estimation of unknown parameters is performed using the maximum likelihood method, and its asymptotic properties are analyzed. In addition, confidence intervals are calculated for GZTP and CGZTP parameters by Wald's method. Based on generated samples, Bayes estimates of unknown parameters and credible intervals are further computed. Simulation studies are performed to assess effectiveness of parameter estimates, while real-world cases illustrate useful applications of the proposed distributions.