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Confidence characteristics of distributions. (English) Zbl 1116.60306

Summary: We introduce the confidence characteristic of a distribution as the distribution corresponding to the decomposition concentration function. We show that the decomposition concentration function has very good differentiability properties for any distribution, that the Lebesgue measures of the shortest confidence regions of a distribution and its confidence characteristic are the same, and that similar properties hold for the entropies and the level sets of their densities.

MSC:

60E05 Probability distributions: general theory
62E10 Characterization and structure theory of statistical distributions
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