Interval Estimation of the Ratio of Scale Parameters for Two Shifted Exponential Populations under Common Location Set-up

Abstract

Under the exponential model, the ratio of the scale parameters corresponds to the hazard ratio, a key measure for comparing reliability across populations. Motivated by this, we study interval estimation for the ratio of scale parameters in two exponential populations with a common location parameter. Several confidence interval methods are developed, including asymptotic-like intervals, MOVER intervals, bootstrap-p and bootstrap-t methods, highest posterior density (HPD) intervals via MCMC, and generalized pivot-based intervals. A simulation study is conducted to evaluate their performance, indicating that the HPD interval performs best in terms of coverage probability and average length. The proposed methods are further illustrated using two real data sets.