The Burr X-Power Lomax Distribution: Properties, Inference, and Applications in Reliability Analysis

Abstract

This study proposes a novel generalized probability distribution, referred to as the Burr X–Power Lomax Distribution (BPLD), by incorporating the Burr X-G family into the Power Lomax distribution. The new distribution enhances the flexibility of the conventional Lomax and Power Lomax models, making it appropriate for analyzing skewed and heavy-tailed data frequently observed in reliability, engineering, survival, and lifetime studies. Key statistical properties of the BPLD are derived, including its probability density function, cumulative distribution function, quantile function, ordinary moments, moment generating function, characteristic function, survival function, and hazard rate function. The model parameters are estimated using the maximum likelihood estimation (MLE) technique. The theoretical findings demonstrate that the proposed distribution is highly flexible and provides an effective alternative for modeling lifetime and reliability data with varying distributional characteristics.