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January, 1977 Distribution and Expected Value of the Rank of a Concomitant of an Order Statistic
H. A. David, M. J. O'Connell, S. S. Yang
Ann. Statist. 5(1): 216-223 (January, 1977). DOI: 10.1214/aos/1176343756


Let $(X_i, Y_i)$ be $n$ independent rv's having a common bivariate distribution. When the $X_i$ are arranged in nondecreasing order as the order statistics $X_{r:n} (r = 1,2,\cdots, n)$, the $Y$-variate $Y_{\lbrack r:n\rbrack}$ paired with $X_{r:n}$ is termed the concomitant of the $r$th order statistic. The small-sample theory of the distribution and expected value of the rank $R_{r:n}$ of $Y_{\lbrack r:n\rbrack}$ is studied. In the special case of bivariate normality an illustrative table of the probability distribution of $R_{r,n}$ is given. A more extensive table of $E(R_{r,n})$ is also provided and it is found that asymptotic results require comparatively small finite-sample corrections even for modest values of $n$. Some applications are briefly indicated.


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H. A. David. M. J. O'Connell. S. S. Yang. "Distribution and Expected Value of the Rank of a Concomitant of an Order Statistic." Ann. Statist. 5 (1) 216 - 223, January, 1977.


Published: January, 1977
First available in Project Euclid: 12 April 2007

zbMATH: 0356.62040
MathSciNet: MR445673
Digital Object Identifier: 10.1214/aos/1176343756

Primary: 62G30
Secondary: 62F07

Keywords: bivariate normal , concomitants , order statistics , ranking , selection , tables

Rights: Copyright © 1977 Institute of Mathematical Statistics

Vol.5 • No. 1 • January, 1977
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