A flexible reliability and performance modeling framework using the unit inverse Lomax distribution

Abstract

The Unit Inverse Lomax Distribution (UILxD) is introduced as a new statistical model tailored for data within the unit interval. This paper explores the theoretical framework of UILxD, presenting closed form expressions for its probability density function, cumulative distribution function, survival function, hazard rate, and quantile function. The model’s flexibility is highlighted through its ability to capture diverse data characteristics, such as skewness, kurtosis, and heavy tails, making it suitable for applications in fields like insurance, finance, and reliability engineering. Key statistical properties, including moments, mode, order statistics, and various entropy measures are derived. Multiple estimation methods—Maximum Likelihood Estimation, Cramer Von Mises, Ordinary andWeighted Least Squares, and Percentile Estimation are investigated through a Monte Carlo simulation study, demonstrating their performance across different sample sizes. The practical utility of UILxD is validated using three real world datasets , where it outperforms established unit interval distributions based on goodness of fit metrics.