Abstract
A nonparametric test for the two-sample scale problem is proposed by considering the subsample medians of three observations. The proposed statistic has the advantage of not requiring the two distribution functions to have a common median, but rather requiring them to have any common quantile of order α , 0 ≤ α ≤ 1 (not necessarily 1 / 2 ), which is assumed to be known. Pitman efficiency considerations indicate that the proposed test performs well relative to tests already existing in the literature for heavy tailed distributions.
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