Summary.
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.
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Received: 31 December 2003, Revised: 22 March 2004,
JEL Classification Numbers:
C40, D40, D80.
Correspondence to: Ted Bergstrom
We thank Ken Binmore and Larry Samuelson for encouragement and suggestments.
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Bagnoli, M., Bergstrom, T. Log-concave probability and its applications. Economic Theory 26, 445–469 (2005). https://doi.org/10.1007/s00199-004-0514-4
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DOI: https://doi.org/10.1007/s00199-004-0514-4