Bayesian estimation for shifted exponential distributions

Abstract Consider m random samples which are independently drawn from m shifted exponential distributions, with respective location parameters θ1, θ2, …, θm and common scale parameter σ. On the basis of the given samples and in a Bayesian framework, we address the problem of estimating the scale parameter σ and the parametric function γ = ∑mi=1 aiθi + bσ. Our proposed Bayesian estimators are compared, via a Monte Carlo study, to the invariant estimators proposed by Madi and Tsui (1990) and Rukhin and Zidek (1985) in terms of risk improvements on the best affine equivariant estimators.