High Order Statistics From Lambert-Topp-Leone Distribution: Statistical Properties and Applications (Statistics, Optimization & Information Computing, 2025)
This paper investigates the statistical properties of high order statistics derived from the Lambert–Topp–Leone(LTL) distribution. The authors establish recurrence relations for both single and product moments of order statistics and explore their application in characterizing the LTL distribution. Comparative analysis is conducted with related distributions, namely the Power Inverted Topp–Leone (PITL) and Topp–Leone Lomax (TLL) distributions. Through simulations, the study examines the impact of parameter variations on the mean and variance of order statistics across different scenarios, highlighting the stability and flexibility of the LTL model. Theoretical results are validated with a real dataset on stress measurements in concrete, where the LTL distribution demonstrates superior goodness-of-fit compared to competing models. The findings underscore the robustness and adaptability of the LTL distribution for modeling lifetime and reliability data, and suggest directions for future research in statistical modeling and inference.