Gamma Zero-Truncated Poisson Distribution with the Minimum Compounded Function
Keywords:Compounding, gamma distribution, Zero-truncated Poisson distributions
The gamma zero-truncated Poisson (GZTP) distribution is introduced in this work as a novel lifetime distribution created by compounding the gamma and zero-truncated Poisson distributions with the minimum function. The proposed distribution’s features are examined, including proofs of its probability density function and cumulative distribution function and formulas for its survival function, hazard function, moment, mean, variance, and quantile. The shape of the GZTP distribution’s hazard function is flexible and can be increasing, decreasing, or unimodal. The estimation process utilizes maximum likelihood. Asymptotic properties of maximum likelihood estimators are studied, and simulations are used to test how well parameter estimation works.
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