ABSTRACT
This chapter presents the recurrence relations, satisfied by the single and product moments of order statistics from a sample of independent and non-identically distributed exponential random variables. It examines how these can be used to address the problem of efficient estimation of the mean under the multiple-outlier model. The chapter discusses various statistics that have been proposed as estimators of the exponential mean. From tables of the mean square error, it shows that the optimal estimator depends on the sample size, the number of outliers, and how these outliers pronounced are. The chapter explains how to efficiently estimate the exponential mean based on a sample of independent exponential random variables which possibly contains one or more outliers. It provides two illustrative examples, and describes extensions to the estimation of location and scale parameters of the double exponential distribution.
