2005/02/28 by Oliver Johnson, Christina Goldschmidt · 1 citation
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Bayesian Methods and Mixture Models #Random Matrices and Applications #math.PR #msc:11B75 #msc:60C05 #msc:60E15
paper · pdf · doi:10.1051/ps:2006008
published as ESAIM Probability and Statistics, vol 10, pages 206-215, 2006
arxiv created 2005/10/12 · openalex publication_date 2006/04/01 · arxiv updated 2009/12/01 · openalex created_date 2020/11/23 · openalex updated_date 2026/07/30
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.