IDEAS home Printed from https://ideas.repec.org/p/duk/dukeec/95-03.html
   My bibliography  Save this paper

Logconcavity versus Logconvexity: A Complete Characterization

Author

Listed:
  • An, Mark Yuying

Abstract

This paper studies aspects of the broad class of log-concave probability distributions that arise in the economics of uncertainty and information. Useful properties of univariate log-concave distributions are proven without imposing differentiability of density functions. We also discuss discrete and multivariate distributions. We propose simple non-parametric testing procedures for log-concavity. The test statistics are constructed to test one of the two implications of log-concavity: increasing hazard rate or new-is-better-than-used (NBU) property. The tests for increasing hazard rate are based on sample information of the normalized spacing of the order statistics. The tests for NBU property fall into the category of Hoeffding's U-statistics. The test procedures are illustrated with well known economic data where log-concavity is usually assumed.

Suggested Citation

  • An, Mark Yuying, 1995. "Logconcavity versus Logconvexity: A Complete Characterization," Working Papers 95-03, Duke University, Department of Economics.
  • Handle: RePEc:duk:dukeec:95-03
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. Flinn, Christopher J & Heckman, James J, 1983. "Are Unemployment and Out of the Labor Force Behaviorally Distinct Labor Force States?," Journal of Labor Economics, University of Chicago Press, vol. 1(1), pages 28-42, January.
    3. Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Imperfect Competition: On the Existence of Equilibrium," Econometrica, Econometric Society, vol. 59(1), pages 25-59, January.
    4. Heckman, James J & Honore, Bo E, 1990. "The Empirical Content of the Roy Model," Econometrica, Econometric Society, vol. 58(5), pages 1121-1149, September.
    5. Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Social Choice: A Mean Voter Theorem," Econometrica, Econometric Society, vol. 59(1), pages 1-23, January.
    6. Burdett, Kenneth & Ondrich, Jan I, 1985. "How Changes in Labor Demand Affect Unemployed Workers," Journal of Labor Economics, University of Chicago Press, vol. 3(1), pages 1-10, January.
    7. Laffont, Jean-Jacques & Tirole, Jean, 1988. "The Dynamics of Incentive Contracts," Econometrica, Econometric Society, vol. 56(5), pages 1153-1175, September.
    8. Burdett, Kenneth, 1996. "Truncated means and variances," Economics Letters, Elsevier, vol. 52(3), pages 263-267, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mark Yuying An, 1996. "Log-concave Probability Distributions: Theory and Statistical Testing," Game Theory and Information 9611002, University Library of Munich, Germany.
    2. Stefano DellaVigna & M. Daniele Paserman, 2005. "Job Search and Impatience," Journal of Labor Economics, University of Chicago Press, vol. 23(3), pages 527-588, July.
    3. Gadat, Sébastien & Panloup, Fabien & Pellegrini, C., 2020. "On the cost of Bayesian posterior mean strategy for log-concave models," TSE Working Papers 20-1155, Toulouse School of Economics (TSE).
    4. Daisuke Oyama & Yasuhiro Sato & Takatoshi Tabuchi & Jacques-François Thisse, 2009. "On the impact of trade on industrial structures: The role of entry cost heterogeneity," Working Papers halshs-00566786, HAL.
    5. Madeleine Cule & Richard Samworth & Michael Stewart, 2010. "Maximum likelihood estimation of a multi‐dimensional log‐concave density," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(5), pages 545-607, November.
    6. Fougère, Denis & Pradel, Jacqueline & Roger, Muriel, 2009. "Does the public employment service affect search effort and outcomes?," European Economic Review, Elsevier, vol. 53(7), pages 846-869, October.
    7. von Thadden, Ernst-Ludwig, 2002. "An incentive problem in the dynamic theory of banking," Journal of Mathematical Economics, Elsevier, vol. 38(1-2), pages 271-292, September.
    8. Anderson, Simon P. & Renault, Regis, 2003. "Efficiency and surplus bounds in Cournot competition," Journal of Economic Theory, Elsevier, vol. 113(2), pages 253-264, December.
    9. Daisuke Oyama & Yasuhiro Sato & Takatoshi Tabuchi & Jacques‐François Thisse, 2011. "On the impact of trade on the industrial structures of nations," International Journal of Economic Theory, The International Society for Economic Theory, vol. 7(1), pages 93-109, March.
    10. Mares, Vlad & Swinkels, Jeroen M., 2011. "Near-optimality of second price mechanisms in a class of asymmetric auctions," Games and Economic Behavior, Elsevier, vol. 72(1), pages 218-241, May.
    11. Gould, Eric D. & Paserman, M. Daniele, 2003. "Waiting for Mr. Right: rising inequality and declining marriage rates," Journal of Urban Economics, Elsevier, vol. 53(2), pages 257-281, March.
    12. Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Social Choice: A Mean Voter Theorem," Econometrica, Econometric Society, vol. 59(1), pages 1-23, January.
    13. Christian Ewerhart & Julia Lareida, 2018. "Voluntary disclosure in asymmetric contests," ECON - Working Papers 279, Department of Economics - University of Zurich, revised Jan 2021.
    14. Nolan, D., 1999. "On min-max majority and deepest points," Statistics & Probability Letters, Elsevier, vol. 43(4), pages 325-333, July.
    15. Daisuke Oyama & Yasuhiro Sato & Takatoshi Tabuchi & Jacques‐François Thisse, 2011. "On the impact of trade on the industrial structures of nations," International Journal of Economic Theory, The International Society for Economic Theory, vol. 7(1), pages 93-109, March.
    16. Richard Rogerson & Robert Shimer & Randall Wright, 2004. "Search-Theoretic Models of the Labor Market-A Survey," NBER Working Papers 10655, National Bureau of Economic Research, Inc.
    17. Denis Fougère & Jacqueline Pradel & Muriel Roger, 2005. "Does Job-Search Assistance Affect Search Effort and Outcomes ? A Microeconometric Analysis of Public Versus Private Search Methods," Working Papers 2005-33, Center for Research in Economics and Statistics.
    18. Foucart, Renaud, 2020. "Metasearch and market concentration," International Journal of Industrial Organization, Elsevier, vol. 70(C).
    19. Keane, Michael P. & Todd, Petra E. & Wolpin, Kenneth I., 2011. "The Structural Estimation of Behavioral Models: Discrete Choice Dynamic Programming Methods and Applications," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.),Handbook of Labor Economics, edition 1, volume 4, chapter 4, pages 331-461, Elsevier.
    20. Hazelton, Martin L., 2011. "Assessing log-concavity of multivariate densities," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 121-125, January.

    More about this item

    JEL classification:

    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:duk:dukeec:95-03. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Department of Economics Webmaster). General contact details of provider: http://econ.duke.edu/ .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.