Bayesian estimation of P(Y > X) in the two-parameter exponential distribution utilizing an initial guess

Abstract

This paper develops a Bayesian approach to estimate the stress-strength reliability, the probability that one random variable exceeds another. The proposed methodology utilizes an initial guess of this reliability through an informative prior, which constitutes the cornerstone of the model. Emphasis lies on exponentially distributed data, but the proposed method is applicable in a wider range of models with similar form of stress-strength reliability. A Monte Carlo simulation study is conducted to compare the performance of the new estimators with both the Maximum Likelihood and the Shrinkage estimators. The comparison is conducted with respect to the Mean Squared Error (MSE) for different values of the rate parameters of the exponential distribution. The proposed method outperforms the two aforementioned alternative methods. A demonstration is conducted through analyzing a real data set.