Reliability Modeling using an Equilibrium-Based Xgamma Distribution: Properties, Estimation, and Applications

Abstract

The equilibrium distribution approach is applied to the existing Xgamma model in this work to develop a new lifetime model known as the Induced Xgamma (i-Xg) distribution.  Because of its adaptable shape properties, the suggested distribution can be used to model heterogeneous and positively skewed lifetime datasets. Probability density and distribution functions, moments, the moment generating function, reliability measures (mean residual life, hazard rate, and reversed hazard), stochastic dominance, entropy measures, inequality curves, and order statistics, including extremes, are among the important analytical properties that we derive.  The model's identifiability is rigorously established. The model parameter is estimated using seven traditional estimation methods: Maximum Likelihood (ML), Least Squares (LS), Weighted LSE (WLS), Cramer-von-Mises (CvM), Maximum Product of Spacings (MPS), Anderson-Darling (AD), and Right-tail AD (RAD).  Their performance is assessed in terms of bias and MSE for varying sample sizes using a Monte-Carlo simulation study.  The suggested i-Xg model provides a better fit than competing distributions, as shown by applications to a variety of real-life datasets, confirming its value in statistical modelling of survival-type and reliability data.