On Poisson Moment Exponential Distribution with Applications

In this study, a one-parameter discrete probability distribution is proposed and studied. The understudy distribution is named “Poisson Moment Exponential distribution”. Mathematical properties of proposed distribution are derived and discussed. For parameter estimation purposes seven different methods maximum likelihood, maximum product spacing, Anderson-Darling, Cramer von-Misses, least-squares, weighted least-squares and right tailed Anderson-Darling are used. The behavior of these estimators is assessed using a Monte Carlo simulation study. Four real datasets from different fields (i.e. failure times, slow-pace students’ marks, epileptic seizure counts, and European corn borer) are used to show the flexibility of the proposed distribution. It is evident that the proposed discrete distribution efficiently analyzed these datasets.