Order statistics from non-identical exponential random variables and some applications

In this paper, we establish some recurrence relations satisfied by the single and product moments of order statistics arising from n independent and non-identically distributed exponential random variables. These recurrence relations will enable one to compute all the single and product moments (for example, means, variances and covariances) of all order statistics in a simple recursive manner. The results for the multiple-outlier model are deduced as special cases. These results are used to address the problem of efficient estimation of the mean of an exponential population when one or more outliers are possibly present in the sample. Finally, we use these results to examine the sensitivity of a ‘robust’ linear estimator to the presence of multiple outliers in the sample.