Improved estimators of hazard rate from a selected exponential population

Abstract

Consider k ( ≥ 2 ) number of independent populations, following two parameter exponential distributions, sharing a common location parameter and unequal scale parameters. The location and scale parameters are assumed to be unknown. We focus into the study of estimation of the hazard rate of a selected population with respect to entropy loss function. Define W i = Z i − Y , where Z i denotes the sample mean of the i-th sample and Y represents the minimum observation of all the samples, for i = 1 , … , k . We select the population with the largest W i . In order to obtain improved estimator, Brewster-Zidek technique is implemented. Further, dominating estimators upon the improved ones are obtained using differential inequality approach. A numerical study of the risk improvements for the proposed estimators has been carried out.