Nakagami–Burr XII Distribution with Application to Real-Life Data

Abstract

This paper presents the new Nakagami-Burr XII distribution, a novel and flexible four-parameter model that extends the classical Burr family by incorporating a Nakagami-inspired structural component. The resulting distribution exhibits a high degree of adaptability, capable of modeling data with pronounced skewness, heavy tails, and non-monotonic hazard functions—characteristics often observed in reliability, survival, and environmental data. Closed-form expressions are derived for the probability density function, cumulative distribution function, and hazard rate function. Parameter estimation is performed using both Maximum Likelihood Estimation (MLE) and the Expectation-Maximization (EM) algorithm, providing robust inference under various data conditions. A detailed Monte Carlo simulation study is conducted to examine the bias, variance, and mean squared error (MSE) of the estimators. Applications to real-world datasets demonstrate the superior fit of the Nakagami-Burr XII distribution compared to existing models, such as the Nakagami-Weibull distribution, based on standard goodness-of-fit metrics. These results highlight the practical utility and modeling flexibility of the proposed distribution, making it a valuable tool for statistical modeling across diverse applied fields.