UMVU Estimation of Reliability Function and Stress–Strength Reliability from Proportional Reversed Hazard Family Based on Lower Records

Abstract

SYNOPTIC ABSTRACTIn this study, we have obtained the uniformly minimum variance unbiased estimator (UMVUE) of reliability function and stress–strength reliability for one parameter proportional reversed hazard rate family of distribution based on lower record values. Further, the results are reduced for power function distribution, exponentiated Weibull distribution, generalized exponential distribution, generalized Rayleigh (also known as Burr type X) distribution and Topp–Leone distribution. Also, the UMVU estimator and maximum likelihood estimator are compared through simulation.