On the exact distribution of linear combinations of order statistics from dependent random variables

Reinaldo B. Arellano-Valle, Marc G. Genton*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

44 Scopus citations

Abstract

We study the exact distribution of linear combinations of order statistics of arbitrary (absolutely continuous) dependent random variables. In particular, we examine the case where the random variables have a joint elliptically contoured distribution and the case where the random variables are exchangeable. We investigate also the particular L-statistics that simply yield a set of order statistics, and study their joint distribution. We present the application of our results to genetic selection problems, design of cellular phone receivers, and visual acuity. We give illustrative examples based on the multivariate normal and multivariate Student t distributions.

Original languageEnglish (US)
Pages (from-to)1876-1894
Number of pages19
JournalJournal of Multivariate Analysis
Volume98
Issue number10
DOIs
StatePublished - Nov 2007

Bibliographical note

Funding Information:
The authors thank two anonymous referees for suggestions that improved the paper. This research was partially supported by Grant FONDECYT 1040865/7050091-Chile and by NSF Grant DMS-0504896.

Keywords

  • Elliptically contoured
  • Exchangeable
  • Fundamental skew distribution
  • Kurtosis
  • Maximum
  • Selection mechanism
  • Skewness

ASJC Scopus subject areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

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