Some Characterizations Based on Generalized Order Statistics from Power Inverted Topp–Leone Distribution

This paper delves into the generalized order statistics of the Power Inverted Topp–Leone (PITL) distribution, along with its special cases, such as order statistics, the rth moment of order statistics, rth L-moment, and trimmed L-moment (TL-moment). A comprehensive analysis is conducted to derive recurrence relations for both the single and product moments of generalized order statistics based on the PITL distribution. These recurrence relations serve as a foundation for understanding the statistical properties and behavior of the PITL distribution under various scenarios. Special cases, including order statistics and record values, are discussed in detail as particular instances of the generalized framework. Additionally, the characterization of the PITL distribution is achieved through the derived recurrence relations for moments, providing valuable insights into its structure and applications. This study contributes to the broader field of statistical theory by enhancing the understanding and utility of the PITL distribution in practical and theoretical contexts.