A new mixed Poisson Komal distribution with application on radiation, agricultural and medical sciences data

A new one-parameter discrete probability model is introduced and explored. The derived model is a mixture of Poisson and Komal distributions, named as Poisson-Komal distribution . We developed and analyzed its key statistical properties, including generating functions, moments, reliability characteristics, mean residual life, Shannon entropy, and expression of order statistics. The parameters of the novel distribution are estimated employing the maximum likelihood estimation technique and Method of Moments, effectively utilizing the unique advantages and capabilities of both techniques to achieve accurate, detailed, and well-rounded estimates of the distribution's parameters. An extensive Monte Carlo simulation study is employed to evaluate the performance of these considered estimation methods for different parameter and sample size choices. The adaptability and flexibility of the proposed count distribution have been demonstrated using three data examples related to radiation, agricultural, and medical sciences. It is exhibited with a superior fit compared to considered competitive count distributions.