Log-concavity of Stirling numbers and unimodality of Stirling distributions
type: Item
instance of: scholarly article
title: Log-concavity of Stirling numbers and unimodality of Stirling distributions
zbMATH Open document ID: 0676.60022
DOI: 10.1007/BF00049427
author: Masaaki Sibuya
published in: Annals of the Institute of Statistical Mathematics
publication date: 1988-01-01T00:00:00Z
review text: A series of inequalities involving Stirling numbers of the first and second kind with adjacent indices are obtained, some of which show log- concavity of Stirling numbers in three directions. Some of them are new, others extend or improve earlier results. These inequalities are used to prove unimodality or strong unimodality of all the subfamilies of Stirling probability functions for any parameter value. They are further applied to obtain Poisson distributions stochastically larger than some of the subfamilies of Stirling probability distributions, to show monotonicity of the convolutions of Stirling numbers and to prove log-concavity of the binomial coefficients.
Mathematics Subject Classification ID: 60E99
Mathematics Subject Classification ID: 11B39
zbMATH DE Number: 4107828
zbMATH Keywords: Stirling numbers
zbMATH Keywords: log-concavity of Stirling numbers
zbMATH Keywords: monotonicity of the convolutions of Stirling numbers
zbMATH Keywords: log-concavity of the binomial coefficients
reviewed by: George N. Philippou
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4107828