Preservation of log-concavity on summation

OT Johnson, CA Goldschmidt

Research output: Contribution to journalArticle (Academic Journal)peer-review

15 Citations (Scopus)

Abstract

We extend Hoggar's theorem that the sum of two independent discrete-valued log-concave random variables is itself log-concave. We introduce conditions under which the result still holds for dependent variables. We argue that these conditions are natural by giving some applications. Firstly, we use our main theorem to give simple proofs of the log-concavity of the Stirling numbers of the second kind and of the Eulerian numbers. Secondly, we prove results concerning the log-concavity of the sum of independent (not necessarily log-concave) random variables.
Translated title of the contributionPreservation of log-concavity on summation
Original languageEnglish
Pages (from-to)206 - 215
Number of pages10
JournalESAIM. Probability and Statistics
Volume10
DOIs
Publication statusPublished - 2006

Bibliographical note

Publisher: ESAIM

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