## The Annals of Statistics

- Ann. Statist.
- Volume 5, Number 5 (1977), 815-1053

### General Distribution Theory of the Concomitants of Order Statistics

#### 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: 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.