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We shall establish several recurrence relations for the single and product moments of order statistics arising from n non-identically distribution. These recurrence relations are simple in nature and could be applied systematically in order to compute all the single and the product moments of order statistics for all values of in a simple recursive manner. The results for the case when the order statistics arise from a multiple-outlier model (with a slippage of observations) from the same distributions as special cases.

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