A comprehensive framework for a novel power fav-jerry distribution with two parameters: Simulation, model evaluation, and engineering applications

This study introduces an innovative two-parameter statistical model called the power Fav-Jerry distribution, which generalizes the original Fav-Jerry formulation. A comprehensive examination of its mathematical characteristics is presented, covering the computation of moments, the location of the mode, the moment-generating function, the mean residual life, as well as inequality measures such as the Bonferroni and Gini indices, and the Lorenz curve. Parameter inference is carried out using the robust maximum likelihood approach. The precision and consistency of the estimators are assessed through a detailed Monte Carlo simulation (MCS) under multiple parameter settings and varying sample sizes. The model’s flexibility and practical relevance are demonstrated by analyzing two engineering datasets, demonstrating its effectiveness in capturing diverse data patterns and its promise for real-world applications.