Interval estimation of stress-strength reliability parameter for exponential-inverted exponential model: Frequentist and Bayesian approaches

This paper introduces the problem of interval estimation for stress strength reliability parameter P(X<Y)‎, ‎where random variables X and Y stand for stress and strength‎, ‎respectively‎. ‎In most of the research papers‎, ‎the authors assumed that X and Y come from the same family of distribution‎. ‎By taking into account some situations arise‎, ‎in this paper we assume that X and Y follow exponential and inverted exponential distributions‎, ‎respectively‎. ‎Our goal is to construct a confidence interval for reliability parameter in this model by using some (approximately) exact and strong methods such as bootstrap‎, ‎generalized and highest posterior distribution approaches‎. ‎Also‎, ‎we compare these methods by means of the expected length and coverage probability criteria‎. ‎Finally‎, ‎a real data set is given and we apply the above methods of estimation on it to inference about the parameter of interest.