Dependence structure of bivariate order statistics with applications to Bayramoglu’s distributions

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

Journal of Multivariate Analysis, 2013, vol. 114, issue C, 201-208

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.

Keywords: Baker’s bivariate distribution; Pearson’s correlation; Positive quadrant dependent; Negative quadrant dependent; Fréchet–Hoeffding bounds; Hoeffding’s representation for covariance (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (4)

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DOI: 10.1016/j.jmva.2012.07.009

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