Economic Theory

, Volume 26, Issue 2, pp 445–469

Log-concave probability and its applications

Symposium Article

DOI: 10.1007/s00199-004-0514-4

Cite this article as:
Bagnoli, M. & Bergstrom, T. Economic Theory (2005) 26: 445. doi:10.1007/s00199-004-0514-4


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.

Keywords and Phrases:

Log-concavity. ReliabilityHazard functionsProbability distributionsFailure ratesCostly appraisalsMean residual lifetime.

Copyright information

© Springer-Verlag Berlin/Heidelberg 2005

Authors and Affiliations

  1. 1.Department of AccountingPurdue UniversityWest LafayetteUSA
  2. 2.Department of EconomicsUC Santa BarbaraSanta BarbaraUSA