Analysis of extropy and entropy measures with the power Lomax distribution: Theory and practical applications

Information measures in statistical distributions have wide-ranging applications in fields such as reliability engineering, information theory, hydrology, and environmental sciences, where understanding variability and risk is essential for decision making and system design. Motivated by this, we investigate and analyze uncertainty measures, namely, entropy and extropy measures, within the framework of the power Lomax distribution (PoLxD), a heavy-tailed model widely used in modeling lifetime and environmental data. We introduce novel formulations of these measures based on the quantile function of the PoLxD, offering a robust and insightful alternative to traditional methods. To evaluate the efficiency and reliability of the proposed estimators of these measures, we conducted an extensive simulation study, assessing performance through bias, mean squared error, and mean relative error. We examined and commented on the outcomes of calculating these measures, their relationship with the distribution’s parameters, and when they decreased and increased. Finally, we validate our approach by applying the proposed uncertainty measures to two real-world datasets where the PoLxD provided a superior fit.