A new generalization of power Chris-Jerry distribution with different estimation methods, simulation and applications

Abstract

The choice of a suitable model has a major impact on the precision and dependability of statistical modeling results. A new model, the transmuted power Chris-Jerry distribution (Tr-PCJD), is presented in this study. The Tr-PCJD is a valuable generalization of the power Chris-Jerry distribution, known for its simplicity and effectiveness in modeling non-negative real-world. Its hazard rate function and density function support a wide variety of designs which reflects this adaptability. Additionally, it includes two existing models as well as a new sub-model. We examine the mathematical characteristics of the Tr-PCJD, such as random number generation, moments, and extropy measures, in order to highlight its significance. Along with that, we investigate eight estimation techniques for estimating the distribution’s unknown parameters. The performance of the Cramer-von Mises, maximum likelihood, right tail Anderson–Darling, least squares, percentiles, Anderson–Darling, weighted least squares, and Anderson–Darling left tail second order estimators is assessed by an extensive simulation study. To further empirically validate the promise of the Tr-PCJD, we apply it to a real-world dataset.