Discrete Poisson Ramos–Louzada Exponential Distribution with Mathematical Properties, and Applications

A new two-parameter mixed Poisson distribution is introduced and explored in this study. The new model is named the Poisson Ramos Louzada Exponential distribution. Various statistical characteristics of the new count distribution are derived and studied, including moments, generating function, overdispersion, failure rate, reversed hazard function, cumulative hazard function, Mills ratio, odd function, and order statistics. A novel regression model is also introduced based on this distribution. The parameters of the new probability model are estimated using the maximum likelihood estimation approach. The estimation behaviour of these derived estimators is studied using a Monte Carlo simulation study. The flexibility and adaptability of the new distribution have been confirmed using two datasets related to radiation and corn borer. It is revealed that the proposed distribution provides efficient results are competitive count models.