Abstract
AbstractDistance between two probability densities or two random variables is a well established concept in statistics. The present paper considers generalizations of distances to separation measurements for three or more elements in a function space. Geometric intuition and examples from hypothesis testing suggest lower and upper bounds for such measurements in terms of pairwise distances; but also in Lp spaces some useful non‐pairwise separation measurements always lie within these bounds. Examples of such separation measurements are the Bayes probability of correct classification among several arbitrary distributions, and the expected range among several random variables.
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