On the unimodality of discrete probability measures
The notion of \(\alpha\)-unimodality [\textit{R. A. Olshen} and \textit{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 \textit{R. Theodorescu}, Math. Ann. 266, 357-367 (1984; Zbl 0525.60019)].
scientific article; zbMATH DE number 4058510