Relations and identities for the moments of order statistics from a sample containing a single outlier

In this paper, we derive several new recurrence relations and indentities satisfied by the single and the product moments of order statistics from a sample of size n in the presence of an outlier. These recurrence relations involve the first two single moments and the product moments in samples of sized n−1 and less. By making use of these recurrence relations we show that it is sufficient to evaluate at most two single rerents and (n−2)/2 …