## The Annals of Mathematical Statistics

### Ratios Involving Extreme Values

W. J. Dixon

#### 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

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