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Majorization, concave entropies, and comparison of experiments. (English) Zbl 0601.62006
The paper under review contains the comparison of different sets of axioms for the notion of entropy for discrete measures. The entropy H is said to be Schur-concave if H(P)\(\leq H(Q)\) whenever \(Q=PT\) where T denotes a Markov morphism. It turns out that Schur concavity is equivalent to various other conditions which are well motivated in information theory. The results can be applied to the comparison of experiments and the Bayes error.
Reviewer: A.Janssen

MSC:
62B10 Statistical aspects of information-theoretic topics
62B15 Theory of statistical experiments
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