Shifted Burr Type XII Distribution for Modeling Asymmetric Lifetime Data

Abstract

This study introduces the four-parameter Shifted Burr Type XII distribution, a mathematical extension of the classical Burr XII model designed to analyze asymmetric lifetime data with a non-zero threshold support restriction. We derive core structural properties of the proposed model, including closed-form expressions for the probability density, cumulative distribution, hazard rate, and quantile functions, as well as raw and incomplete moments and various entropy measures. Analytical expressions for single-component and multi-component stress-strength reliability profiles are also established. Parameter estimation is evaluated using fifteen classical non-Bayesian methods. An extensive Monte Carlo simulation study demonstrates consistent monotonic convergence of the absolute bias and root mean square error toward zero as the sample size increases, identifying maximum likelihood estimation and maximum product of spacings estimation as the most asymptotically stable and efficient frameworks. The empirical applicability of the Shifted Burr Type XII distribution is validated using two datasets representing patient hospital waiting times and the mortality rate of children in Japan. Goodness-of-fit assessments demonstrate that the proposed distribution significantly outperforms traditional benchmarks, including the classical Burr XII and Weibull models, establishing its superior modeling flexibility for asymmetric lifetime data.