2005
DOI: 10.1007/s00199-004-0514-4
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Log-concave probability and its applications

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 … Show more

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Cited by 1,021 publications
(300 citation statements)
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“…The resulting model is as follows: , carried out by the way of the likelihood maximum method with a subsequent log-probability function (Bagnoli and Bergstrom 2005):…”
Section: Methodsmentioning
confidence: 99%
“…The resulting model is as follows: , carried out by the way of the likelihood maximum method with a subsequent log-probability function (Bagnoli and Bergstrom 2005):…”
Section: Methodsmentioning
confidence: 99%
“…Consider X and Y independent variables with log-concave densities f X and f Y , which is satisfied by most common distributions (Bagnoli and Bergstrom 2005). This implies that X and Y have log-concave survival functions F X and F Y (Prékopa 1971(Prékopa , 1973.…”
Section: Discussionmentioning
confidence: 99%
“…10 If the density function F 0 is log-concave, then the distribution function F and the survival function 1−F are log-concave. See Burdett and Wright (1998) and Bagnoli and Bergstrom (2005) for details. Proposition 1 states that the price posting curve is downward sloping if the density function F 0 is log-concave.…”
Section: Proposition 1 Each Seller Postsmentioning
confidence: 99%
“…It is important to emphasize that the price posting game is not responsible for the nonWalrasian outcome; the model with observable valuations and bilateral bargaining also leads to the non-Walrasian outcome. 4 As applications of the basic model, this paper considers various forms of market structure. In the basic model, each seller ignores how her price will influence the buyers' willingness to trade through its impact on their values of search (or, the values of their options to wait).…”
Section: Introductionmentioning
confidence: 99%
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