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Log-concave probability and its applications

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Author Info
Mark Bagnoli ()
Ted Bergstrom ()

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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. Copyright Springer-Verlag Berlin/Heidelberg 2005

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File URL: http://hdl.handle.net/10.1007/s00199-004-0514-4
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Publisher Info
Article provided by Springer in its journal Economic Theory.

Volume (Year): 26 (2005)
Issue (Month): 2 (08)
Pages: 445-469
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Handle: RePEc:spr:joecth:v:26:y:2005:i:2:p:445-469

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Related research
Keywords: Log-concavity. Reliability; Hazard functions; Probability distributions; Failure rates; Costly appraisals; Mean residual lifetime.;

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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  2. Armstrong, Mark, 2006. "Price discrimination," MPRA Paper 4693, University Library of Munich, Germany. [Downloadable!]
  3. Bergstrom, Theodore C & Bagnoli, Mark, 1993. "Courtship as a Waiting Game," Journal of Political Economy, University of Chicago Press, vol. 101(1), pages 185-202, February. [Downloadable!] (restricted)
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  4. Bagnoli, Mark & Khanna, Naveen, 1991. "Buyers' and Sellers' Agents in the Housing Market," The Journal of Real Estate Finance and Economics, Springer, vol. 4(2), pages 147-56, June.
  5. Hanming Fang & Peter Norman, 2003. "To Bundle or Not to Bundle," Cowles Foundation Discussion Papers 1440, Cowles Foundation, Yale University. [Downloadable!]
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  6. Steven A. Matthews, 1985. "Comparing Auctions for Risk Averse Buyers: A Buyer's Pointof View," Discussion Papers 664R, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
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  7. Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Imperfect Competition: On the Existence of Equilibrium," Econometrica, Econometric Society, vol. 59(1), pages 25-59, January. [Downloadable!] (restricted)
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  8. Ilya Segal, 2003. "Optimal Pricing Mechanisms with Unknown Demand," American Economic Review, American Economic Association, vol. 93(3), pages 509-529, June. [Downloadable!]
  9. Myerson, Roger B. & Satterthwaite, Mark A., 1983. "Efficient mechanisms for bilateral trading," Journal of Economic Theory, Elsevier, vol. 29(2), pages 265-281, April. [Downloadable!] (restricted)
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  10. Chowdhry, Bhagwan & Jegadeesh, Narasimhan, 1994. "Pre-Tender Offer Share Acquisition Strategy in Takeovers," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 29(01), pages 117-129, March. [Downloadable!]
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  12. Laffont, Jean-Jacques & Tirole, Jean, 1988. "The Dynamics of Incentive Contracts," Econometrica, Econometric Society, vol. 56(5), pages 1153-75, September. [Downloadable!] (restricted)
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  13. Michael H. Riordan & David E.M. Sappington, 1989. "Second Sourcing," RAND Journal of Economics, The RAND Corporation, vol. 20(1), pages 41-58, Spring. [Downloadable!] (restricted)
  14. Weber, Shlomo, 1992. "On Hierarchical Spatial Competition," Review of Economic Studies, Blackwell Publishing, vol. 59(2), pages 407-25, April. [Downloadable!] (restricted)
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  16. Eric Maskin & John Riley, 1984. "Monopoly with Incomplete Information," RAND Journal of Economics, The RAND Corporation, vol. 15(2), pages 171-196, Summer. [Downloadable!] (restricted)
  17. repec:att:wimass:1920318 is not listed on IDEAS
  18. HAIMANKO, Ori & LE BRETON, Michel & WEBER, Shlomo, 2003. "Transfers in a Polarized Country : Bridging the Gap between Efficiency and Stability," IDEI Working Papers 208, Institut d'Économie Industrielle (IDEI), Toulouse. [Downloadable!]
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  20. Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Social Choice: A Mean Voter Theorem," Econometrica, Econometric Society, vol. 59(1), pages 1-23, January. [Downloadable!] (restricted)
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  21. An, Mark Yuying, 1998. "Logconcavity versus Logconvexity: A Complete Characterization," Journal of Economic Theory, Elsevier, vol. 80(2), pages 350-369, June. [Downloadable!] (restricted)
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