On Estimation of Reliability Functions using Record values from Proportional Hazard Rate Model

Abstract

Two measures of reliability functions, namely R(t)=P(X>t) and P=P(X<Y) have been studied based on record values from proportional hazard rate model (PHR) model. For estimation of P, we generalize the results of Basirat et al. (2016) when X and Y belong to different family of distributions from PHR model. Uniformly minimum variance unbiased estimator (UMVUE), maximum likelihood estimator (MLE) and Bayes estimator (BS) are obtained for the powers of the parameter and reliability functions. Simulation studies and a real data example have been presented for illustrative purposes. Asymptotic and exact confidence intervals of the parameters and reliability functions are constructed. Testing procedures are also developed for various hypotheses.