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September 1995 Joint distribution of maxima of concomitants of subsets of order statistics
S.N. Joshi, H.N. Nagaraja
Bernoulli 1(3): 245-255 (September 1995). DOI: 10.3150/bj/1193667817


Let (Xi:n, Y[i:n]), 1≤i≤n, denote the n pairs obtained by ordering a random sample of size n from an absolutely continuous bivariate population on the basis of X sample values. Here Y[i:n] is called the concomitant of the ith order statistic. For 1≤k≤n, let V1=max{{Y[n-k+1:n],...,Y[n:n]} and V2=max{Y[1:n],...,Y[n-k:n]}. In this paper, we discuss the finite-sample and asymptotic joint distribution of (V1,V2). The asymptotic results are obtained when k=[np], 0<p<1, and when k is held fixed, as n→∞. We apply our results to the bivariate normal population and indicate how they can be used to determine k such that V1 is close to Yn:n, the maximum of the values of Y in the sample.


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S.N. Joshi. H.N. Nagaraja. "Joint distribution of maxima of concomitants of subsets of order statistics." Bernoulli 1 (3) 245 - 255, September 1995.


Published: September 1995
First available in Project Euclid: 29 October 2007

zbMATH: 0836.62038
MathSciNet: MR1363540
Digital Object Identifier: 10.3150/bj/1193667817

Keywords: Bivariate normal distribution , concomitants of order statistics , Convergence in distribution , extreme values maximum

Rights: Copyright © 1995 Bernoulli Society for Mathematical Statistics and Probability

Vol.1 • No. 3 • September 1995
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