A novel discrete distribution for modeling medical experimental data and mammalian cytogenetic dosimetry lesion data

In this study, a new discrete Poisson XShanker distribution is derived by mixing Poisson and XShanker distributions. Many statistical properties, including moments and associated measures, survival function, hazard function, mean residual life, and Shannon entropy, are generated and investigated. The model parameter is estimated using the maximum likelihood estimation and the method of moments. The Monte Carlo simulation study is used to evaluate the behavior of the generated estimator. We also introduced a zero-inflated Poisson XShanker distribution to analyze datasets with extensive numbers of zeros. Four datasets from various sectors are used to show the suggested distribution's flexibility and applicability.