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On the unimodality of discrete probability measures. (English) Zbl 0648.60013

The notion of \(\alpha\)-unimodality [R. A. Olshen and L. I. Savage, J. Appl. Probab. 7, 21-34 (1970; Zbl 0193.451)] is adapted to probability measures on \({\mathbb{Z}}\). It is shown that discretely \(\alpha\)- unimodal probability measures on \({\mathbb{Z}}\) can be obtained as projections of \(\alpha\)-unimodal probability measures on \({\mathbb{R}}\). Furthermore, the set of discretely \(\alpha\)-unimodal probability measures on \({\mathbb{Z}}\) has a certain structure leading to a representation theorem of Choquet-Meyer- type [the author and R. Theodorescu, Math. Ann. 266, 357-367 (1984; Zbl 0525.60019)].
Reviewer: E.M.J.Bertin

MSC:

60E05 Probability distributions: general theory
46A55 Convex sets in topological linear spaces; Choquet theory
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References:

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