A new discrete Burr III distribution for modeling radiation and biological data

Abstract

A new three-parameter discrete probability distribution entitled “discrete modified Burr III” distribution is introduced using the survival discretization approach. We derived and explored various statistical properties such as moments, dispersion index, mean deviation, and order statistics. Additionally, we also explore its reliability characteristics including survival, hazard function, cumulative hazard function, and residual reliability function. The parameters of the model are estimated using the maximum likelihood estimation approach. A detailed Monte Carlo simulation is utilized to assess the performance of derived estimators across varying sample sizes. The utility of the new model is evaluated using biological and radiation datasets, demonstrating its better fit compared to considered competing discrete distribution. Additionally, we also analyzed these datasets using the Bayesian estimation approach.