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 $n \leqq 30$.
Citation
W. J. Dixon. "Ratios Involving Extreme Values." Ann. Math. Statist. 22 (1) 68 - 78, March, 1951. https://doi.org/10.1214/aoms/1177729693
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