Refining estimation techniques for the Two-Sided Power Distribution: A data-sensitive perspective

Abstract

This study proposes a novel method aimed at achieving more reliable parameter estimates for the Two-Sided Power Distribution (TSPD), particularly under small-sample conditions. The proposed approach enhances the flexibility and data sensitivity of the distribution by redefining it as a convex combination of two independent uniform components. A new estimation formula is introduced for the probability P r { Y < X } , which holds critical importance in fields such as system reliability and stress–strength modeling. Compared to classical theoretical expressions, this new formulation produces more accurate and stable results in small-sample settings. Simulation studies and real-data applications demonstrate that the proposed method reduces estimation error and yields values closer to empirical observations. Furthermore, the method provides a balanced and computationally feasible alternative to conventional techniques such as maximum likelihood estimation. The results reveal that the proposed approach offers a significant advantage for the reliable computation of key performance metrics such as reliability probabilities and related measures.