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Concentration comparisons between probability measures. (English) Zbl 0765.62021

Summary: We deal with the concept of concentration of a probability measure with respect to another probability measure, when both of them are defined on the same probability space. More precisely, we aim to focus on concentration comparison within a class of probability measures, by using the concept of mean equalizing transfer. It is shown that the resulting ordering coincides with the “natural” one based on concentration functions. Then, on the grounds of suitable extensions of a few classical results, the paper states the equivalence between the above-mentioned ordering and some other interesting conditions.

MSC:

62E10 Characterization and structure theory of statistical distributions
62B99 Sufficiency and information
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