Explicit Expressions for Single and Product Moments of Lower Generalized Order Statistics from Log Logistic Distribution and its Characterization

Current paper comprehensively establishes exact expressions for both single and product moments of lower generalized order statistics originating from scaled log-logistic distributions, popularly recognized as the Fisk Distribution-a distribution extensively utilized in reliability theory. Furthermore, we provide a characterization result for this specific class of distributions, employing the renowned Ruiz identity. This work aims to provide a thorough understanding of the statistical properties of lower generalized order statistics in relation to scaled log-logistic distributions, thereby enhancing the applicability and insights into reliability analysis and related fields..