ESTIMATING THE STRESS-STRENGTH PARAMETER OF LOG-UNIFORM DISTRIBUTIONS AND ITS APPLICATIONS IN EDUCATIONAL PSYCHOLOGY AND ELECTRICAL ENGINEERING

Abstract

In this paper, we develop and analyze estimators of the stress-strength parameter for log-uniform distributions, with applications in both educational psychology and electrical engineering. Specifically, we propose a shrinkage estimator of the stress-strength parameter, constructed based on its maximum likelihood estimator and uniformly minimum variance unbiased estimator. A comprehensive simulation study is conducted to assess the behavior of these estimators. As practical applications, we investigate the effect of coffee consumption on students performance in statistics exams and analyze the degradation behavior of lithium-ion batteries under different thermal storage conditions by estimating the stress-strength parameter from real datasets. The results demonstrate the effectiveness of the proposed estimators and provide meaningful insights into these diverse fields.