Complementary Gamma Zero-Truncated Poisson Distribution and Its Application

Numerous lifetime distributions have been developed to assist researchers in various fields. In this paper, a new continuous three-parameter lifetime distribution is proposed by combining the distribution of the maximum of a sequence of independently identical gamma-distributed random variables with zero-truncated Poisson random variables, defined as the complementary gamma zero-truncated Poisson distribution (CGZTP). The proposed distribution's properties, including proofs of the probability density function, cumulative distribution function, survival function, hazard function, and moments, are discussed. The unknown parameters are estimated using the maximum likelihood method, whose asymptotic properties are examined. In addition, Wald confidence intervals are constructed for the CGZTP parameters. Simulation studies are conducted to evaluate the efficacy of parameter estimation, and a real-world application demonstrates the application of the proposed distribution.