Preservation of log-concavity on summation

Details Preservation of log-concavity on summation Preservation of log-concavity on summation

2005-02-25

arxiv.org/abs/math/0502548v2

ESAIM Probability and Statistics, vol 10, pages 206-215, 2006

Mathematics

Probability

Scientific paper

10.1051/ps:2006008

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.

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