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A probability inequality for ranges and its application to maximum range test procedures. (English) Zbl 0693.62029

Summary: It is proved that for any fixed argument the sequence \((P_ k)\) of the distribution functions of the ranges of k i.i.d. univariate random variables is log-concave if the random variables have a log-concave density. If the support of the distribution is an infinite interval and the density is monotonous then the theorem holds also with “log-convex” instead of “log-concave”. The resulting inequalities can be used by a quick algorithm for closed maximum range test procedures for all pairwise comparisons. Under the above assumptions the application of this algorithm can be extended e.g. to pairwise comparisons of variances.

MSC:

62F03 Parametric hypothesis testing
60E15 Inequalities; stochastic orderings
62J15 Paired and multiple comparisons; multiple testing
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References:

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