Covariance between variables and their order statistics for multivariate normal variables

Yosef Rinott*, Ester Samuel-Cahn

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

Abstract

Siegel (1993, J. Amer. Statist. Assoc. 88, 77-80) showed that when (X1, ..., Xn) have a multivariate normal distribution then Cov(X1, X(1)) = Σni = 1 Cov(X1, Xi)P(Xi = X(1)), where X(1) is the minimum of (X1, ..., Xn). 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.

Original languageEnglish
Pages (from-to)153-155
Number of pages3
JournalStatistics and Probability Letters
Volume21
Issue number2
DOIs
StatePublished - 23 Sep 1994
Externally publishedYes

Keywords

  • Multivariate normal
  • Order statistics

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