Inference on Stress-Strength Reliability from Topp-Leone Distributions

Our goal is to estimate the probability R = P(Y X) when X and Y are independent random variables following Topp-Leone distribution with different scale parameters. We study the ML estimator R of R, establish its asymptotic properties and construct confidence intervals. Assuming that the shape parameter is known, we study both the ML and Bayes estimators of R, and find confidence intervals. Simulation study has been presented for illustrative purposes.