On the estimation of stress strength reliability parameter of inverted exponential distribution

Abstract

This paper aims to estimate the stress-strength reliability parameter R = P(Y < X), when X and Y are independent inverted exponential random variable. We have also discussed some fundamental properties of the considered distribution. The maximum likelihood estimator (MLE) of R and its asymptotic distribution are obtained. The Bayesian estimation of the reliability parameter has been also discussed under the assumption of independent gamma prior. Numerical integration technique is used for Bayesian computation. The proposed estimators are compared in terms of their mean squared errors through the simulation study. Two real data sets representing survival of head and neck cancer patients are fitted using the inverted exponential distribution and used to estimate the stress-strength parameters and reliability.