Non-Bayesian and Bayesian estimation of stress-strength reliability from Topp-Leone distribution under progressive first-failure censoring

In this paper, the Bayesian and non-Bayesian estimation of psi = P(X > Y) based on the progressively first-failure censored data is considered. The X and Y are strength and stress random variables and follow the Topp-Leone distributions, respectively. The maximum likelihood and Bayes estimators of psi are derived. The Bayes estimators under generalized entropy loss function are computed using Lindley's approximation and Gibbs sampling methods. Different interval estimates like asymptotic, bootstrap confidence, Bayesian credible, and highest posterior density credible intervals of psi are constructed. Furthermore, a Monte Carlo numerical study is conducted to check the performance of various estimators developed. Finally, an application of algorithm real data is considered for illustrative purposes.