## The Annals of Mathematical Statistics

- Ann. Math. Statist.
- Volume 22, Number 1 (1951), 68-78.

### Ratios Involving Extreme Values

#### Abstract

Ratios of the form $(x_n - x_{n-j})/(x_n - x_i)$ for small values of $i$ and $j$ and $n = 3, \cdots, 30$ are discussed. The variables concerned are order statistics, i.e., sample values such that $x_1 < x_2 < \cdots < x_n$. Analytic results are obtained for the distributions of these ratios for several small values of $n$ and percentage values are tabled for these distributions for samples of size $n \leqq 30$.

#### Article information

**Source**

Ann. Math. Statist., Volume 22, Number 1 (1951), 68-78.

**Dates**

First available in Project Euclid: 28 April 2007

**Permanent link to this document**

https://projecteuclid.org/euclid.aoms/1177729693

**Digital Object Identifier**

doi:10.1214/aoms/1177729693

**Mathematical Reviews number (MathSciNet)**

MR39953

**Zentralblatt MATH identifier**

0044.14604

**JSTOR**

links.jstor.org

#### Citation

Dixon, W. J. Ratios Involving Extreme Values. Ann. Math. Statist. 22 (1951), no. 1, 68--78. doi:10.1214/aoms/1177729693. https://projecteuclid.org/euclid.aoms/1177729693