Inferences on Stress-Strength Reliability from Weighted Lindley Distributions

Abstract

This article deals with the estimation of the stress-strength parameter R = P(Y < X), when X and Y are two independent weighted Lindley random variables with a common shape parameter. The MLEs can be obtained by maximizing the profile log-likelihood function in one dimension. The asymptotic distribution of the MLEs are also obtained, and they have been used to construct the asymptotic confidence interval of R. Bootstrap confidence intervals are also proposed. Monte Carlo simulations are performed to verify the effectiveness of the different estimation methods, and data analysis has been performed for illustrative purposes.