On the unimodality of discrete probability measures
type: Item
instance of: scholarly article
title: On the unimodality of discrete probability measures
zbMATH Open document ID: 0648.60013
DOI: 10.1007/BF01162000
author: Radu Theodorescu
author: Emile M. J. Bertin
published in: Mathematische Zeitschrift
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/174040
review text: 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)].
Mathematics Subject Classification ID: 60E05
Mathematics Subject Classification ID: 46A55
zbMATH DE Number: 4058510
zbMATH Keywords: discrete unimodality
zbMATH Keywords: discrete distribution function
zbMATH Keywords: unimodal distribution function
zbMATH Keywords: representation theorem
reviewed by: Emile M. J. Bertin
MaRDI profile type: Publication
cites work: On Discrete oc–Unimodality
cites work: Some characterizations of discrete unimodality
cites work: On characterizations of unimodality of discrete distributions
cites work: Q3918541
cites work: Some Results for Discrete Unimodality
cites work: Note on the moment-problem for unimodal distributions when one or both terminals are known
cites work: On the unimodality of discrete distributions
cites work: A generalized unimodality
cites work: On the unimodality of infinitely divisible distribution functions
OpenAlex ID: W2087481024
description: scientific article; zbMATH DE number 4058510