Jackknife and bootstrap estimation of reliability function in an exponential distribution

Abstract

We propose several estimators of the reliability function R(t) of the two-parameter exponential distribution. We show that the proposed estimators are consistent and compare the proposed estimators by the mean square errors (MSE) through Monte Carlo Method. The proposed jackknife estimator is more efficient than the other estimators in the sense of the MSE when R(t) is small, but the bootstrap bias corrected estimator is more efficient than the other estimators in the sense of the MSE when R(t) is large.