Interval estimation for the Gini index of shifted exponential distribution under Type-II double censoring

Abstract

Given a shifted exponential distribution, the exact sampling distribution of the Gini index has been derived by Moothathu (Ann Inst Stat Math 37: 473–479, 1985). However, direct derivation of confidence interval of the Gini index via inverting the sampling distribution requires highly intensive computational power. In this note, we propose an exact interval estimation procedure through the concept of generalized confidence interval introduced by Weerahandi (J Am Stat Assoc 88: 899–905, 1993). The proposed method is much more computationally efficient and can be readily extended for Type-II doubly censored data. The idea is further developed for the interval estimation of the difference of Gini indexes from two shifted exponential distributions. Numerical studies show that the generalized interval estimator is better than commonly used asymptotic approximation and bootstrap in term of coverage probability, particularly for small to median sample size. The proposed approaches are illustrated via an application to a previously published data set.