Dependence structure of bivariate order statistics with applications to bayramoglu's distributions

J. S. Huang, Xiaoling Dou, Satoshi Kuriki, G. D. Lin

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

We study the dependence structure of bivariate order statistics from bivariate distributions, and prove that if the underlying bivariate distribution H is positive quadrant dependent (PQD) then so is each pair of bivariate order statistics. As an application, we show that if H is PQD, the bivariate distribution K(n)+, recently proposed by Bairamov and Bayramoglu (2012) [1], is greater than or equal to Baker's (2008) [2] distribution H(n)+, and hence K(n)' attains a correlation higher than that of H(n)+. We give two explicit forms of the intractable K(n)+ and prove that for all n ≥ 2, K(n)+ is PQD regardless of H. We also show that if H is PQD, K(n)+ converges weakly to the Fréchet-Hoeffding upper bound as n tends to infinity.

Original languageEnglish
Pages (from-to)201-208
Number of pages8
JournalJournal of Multivariate Analysis
Volume114
Issue number1
DOIs
Publication statusPublished - 2013 Jan 1
Externally publishedYes

Keywords

  • Baker's bivariate distribution
  • Fréchet-hoeffding bounds
  • Hoeffding's representation for covariance
  • Negative quadrant dependent
  • Pearson's correlation
  • Positive quadrant dependent

ASJC Scopus subject areas

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

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