Distribution of concomitants of order statistics and their order statistics |
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Authors: | Qinying He H.N. Nagaraja |
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Affiliation: | 1. Research Institute of Economics and Management, Southwestern University of Finance and Economics, Chengdu, Sichuan 610074, China;2. Department of Statistics, The Ohio State University, 1958 Neil Ave, Columbus, OH 43210, USA |
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Abstract: | For a random sample of size n from an absolutely continuous random vector (X,Y), let Yi:n be ith Y-order statistic and Y[j:n] be the Y-concomitant of Xj:n. We determine the joint pdf of Yi:n and Y[j:n] for all i,j=1 to n, and establish some symmetry properties of the joint distribution for symmetric populations. We discuss the uses of the joint distribution in the computation of moments and probabilities of various ranks for Y[j:n]. We also show how our results can be used to determine the expected cost of mismatch in broken bivariate samples and approximate the first two moments of the ratios of linear functions of Yi:n and Y[j:n]. For the bivariate normal case, we compute the expectations of the product of Yi:n and Y[i:n] for n=2 to 8 for selected values of the correlation coefficient and illustrate their uses. |
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Keywords: | Order statistics Concomitants Joint distribution Correlation coefficient Bivariate normal Broken samples |
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