Estimating a Quantile of an Exponential Distribution

Abstract

We consider the problem of estimating a quantile ξ + b σ of an exponential distribution on the basis of a random sample of size n ≥ 2. Here ξ and σ are unknown location and scale parameters and b is a given constant. For quadratic loss, it is established that the best equivariant estimator is inadmissible if 0 ≤ b < n -1 or b > 1 + n 1 . For b > 1 + n 1 the estimator elsewhere, provides a noticeable improvement over δ 0 .