On Estimation of P(Y < X) for Generalized Inverted Exponential Distribution Based on Hybrid Censored Data

Based on the hybrid censored samples, this article deals with the problem of point and interval estimation of the stress-strength reliability R = P(Y < X) when X and Y both have independent generalized inverted exponential distributions with different shape and common scale parameters. The maximum likelihood estimation, Bayes estimation and parametric bootstrap methods are used for estimating R. Also, asymptotic confidence interval of R is derived based on the asymptotic distribution of R. Bayesian estimation procedure is carried out using Lindley approximation and Markov Chain Monte Carlo methods. Bayes estimate and the HPD credible interval of R are obtained using non-informative and gamma informative priors. A Monte Carlo simulation study is carried out for comparing the different proposed estimation methods. Finally, a pair of real data sets is analyzed for illustration purposes.