Analysis of radiation and corn borer data using discrete Poisson Xrama distribution

In this study, a new one-parameter count distribution is introduced by compounding Poisson and Xrama distributions. The Poisson Xrama (PXr) distribution is a tractable addition to probabilistic modeling, merging the robustness of the Poisson distribution with the flexibility of the Xrama distribution, offering a versatile framework for analyzing count data. We derived and explored its key statistical properties. The mean and variance show a decreasing pattern with an increase in parameter values. The model parameter is estimated via maximum likelihood, moment matching, and Bayesian estimation approaches. A detailed simulation study is utilized to illustrate the behavior of derived estimators. The maximum likelihood approach outperforms the method of moments in terms of accuracy and precision across different sample sizes and parameter choices. The flexibility and applicability of the new count model are accessed using two datasets about European corn borer and cytogenetic dosimetry lesions. It is identified that the new count model efficiently analyzed both datasets as compared to considered competitive distributions.