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Log-concave probability and its applications


  • Mark Bagnoli


  • Ted Bergstrom



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. Copyright Springer-Verlag Berlin/Heidelberg 2005

Suggested Citation

  • Mark Bagnoli & Ted Bergstrom, 2005. "Log-concave probability and its applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(2), pages 445-469, August.
  • Handle: RePEc:spr:joecth:v:26:y:2005:i:2:p:445-469 DOI: 10.1007/s00199-004-0514-4

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