Abstract
Siegel (1993, J. Amer. Statist. Assoc. 88, 77–80) showed that when ( X 1, …, X n ) have a multivariate normal distribution then Cov( X 1, X (1)) = Σ n i = 1 Cov( X 1, X i ) P( X i = X (1)), where X (1) is the minimum of ( X 1, …, X n ). We show that a similar result holds for any order statistic. Thus X (1) can be replaced by X ( r) , the rth order statistic, everywhere in the above formula. Normality is essentially also necessary for this result to hold.
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