The Induced Lomax Distribution: Properties, Estimations, Simulation and Applications

The Induced Lomax Distribution

Abstract

This paper presents the induced Lomax (ILO) distribution, a new one-parameter modification of the standard Lomax model, aimed at enhancing the modeling of lifetime and reliability data. The significance of the ILO distribution is in its adaptability to include heavy-tailed phenomena and various hazard rate configurations, rendering it appropriate for industrial and environmental datasets that encompass extreme events. We establish many mathematical features, encompassing moments, inverse moments, moment-generating functions, quantile functions, and Rényi and Tsallis entropies. Reliability functions, including survival, hazard rate, and reversed hazard rate, are also included. Six estimation techniques maximum likelihood, least squares, weighted least squares, Cramér–von Mises, Anderson–Darling, and percentile methods are utilized to estimate the model parameter. A thorough Monte Carlo simulation is performed to assess bias and mean square error, demonstrating that the Anderson–Darling estimator yields the most precise findings across various sample sizes. Ultimately, two empirical datasets from industrial and environmental contexts are examined to demonstrate the model's enhanced fit relative to alternative distributions. The findings underscore the ILO distribution as a reliable and adaptable instrument for professionals engaged in dependability modeling and extreme value analysis.