The Annals of Statistics

General Distribution Theory of the Concomitants of Order Statistics

S. S. Yang

Full-text: Open access

Abstract

Let $(X_i, Y_i) (i = 1, 2, \cdots, n)$ be $n$ independent $\mathrm{rv}$'s from some bivariate distribution. If $X_{r:n}$ denotes the $r$th ordered $X$-variate, then the $Y$-variate $Y_{\lbrack r:n\rbrack}$ paired with $X_{r:n}$ is termed the concomitant of the $r$th order statistics. The exact and asymptotic distribution theory of $Y_{\lbrack r:n\rbrack}$ and of its rank are studied. The results obtained are applied to a prediction problem in a Round Robin tournament.

Article information

Source
Ann. Statist. Volume 5, Number 5 (1977), 996-1002.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
http://projecteuclid.org/euclid.aos/1176343954

JSTOR
links.jstor.org

Digital Object Identifier
doi:10.1214/aos/1176343954

Mathematical Reviews number (MathSciNet)
MR501519

Zentralblatt MATH identifier
0367.62017

Subjects
Primary: 62E15: Exact distribution theory
Secondary: 62G30: Order statistics; empirical distribution functions 62F07: Ranking and selection

Keywords
Order statistics concomitants distribution Round Robin tournament

Citation

Yang, S. S. General Distribution Theory of the Concomitants of Order Statistics. The Annals of Statistics 5 (1977), no. 5, 996--1002. doi:10.1214/aos/1176343954. http://projecteuclid.org/euclid.aos/1176343954.


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