Log-concave probability and its applications

Ted Bergstrom, University of California, Santa Barbara
Mark Bagnoli, Purdue University

Abstract

In many applications,assumptions about the log-concavity of a probability distribution allow just enough special structure to yield a workable theory.This paper catalogs a series of theorems relating log-concavity and/or log-convexity of probability density functions,distribution functions,reliability functions,and their integrals. We list a large number of commonly-used probability distributions and report the log-concavity or log-convexity of their density functions and their integrals.We also discuss a variety of applications of log-concavity that have appeared in the literature.