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

Area of Science:

• Statistics
• Probability Theory
• Reliability Engineering

Background:

• The Two-Sided Power Distribution (TSPD) is utilized in various fields, but parameter estimation can be challenging, especially with limited data.
• Classical estimation methods may lack accuracy and stability in small-sample scenarios, impacting critical applications like system reliability and stress-strength modeling.

Purpose of the Study:

• To develop a novel and more reliable method for estimating parameters of the Two-Sided Power Distribution (TSPD).
• To introduce an improved estimation formula for probability calculations crucial in reliability and stress-strength analysis.
• To enhance the flexibility and data sensitivity of the TSPD model.

Main Methods:

• Redefining the TSPD as a convex combination of two independent uniform components.
• Developing a new estimation formula for probability calculations.
• Conducting simulation studies and applying the method to real-world data.

Main Results:

• The proposed method yields more accurate and stable parameter estimates compared to classical theoretical expressions, particularly in small-sample settings.
• Simulation studies and real-data applications confirm reduced estimation error and closer alignment with empirical observations.
• The new formulation provides a computationally feasible and balanced alternative to methods like maximum likelihood estimation.

Conclusions:

• The novel estimation method offers significant advantages for computing key performance metrics, including reliability probabilities.
• The approach enhances the reliability and accuracy of TSPD parameter estimation, especially under data constraints.
• This work provides a valuable tool for researchers and practitioners in reliability engineering and related fields.