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Logconcavity versus Logconvexity: A Complete Characterization

  • An, Mark Yuying

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.

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Paper provided by Duke University, Department of Economics in its series Working Papers with number 95-03.

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Date of creation: 1995
Date of revision:
Publication status: Published in JOURNAL OF ECONOMIC THEORY, Vol. 80, 1998, pages 350-369
Handle: RePEc:duk:dukeec:95-03
Contact details of provider: Postal: Department of Economics Duke University 213 Social Sciences Building Box 90097 Durham, NC 27708-0097
Phone: (919) 660-1800
Fax: (919) 684-8974
Web page: http://econ.duke.edu/

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  1. Heckman, James J & Honore, Bo E, 1990. "The Empirical Content of the Roy Model," Econometrica, Econometric Society, vol. 58(5), pages 1121-49, September.
  2. Bergstrom, T. & Bagnali, M., 1991. "Courtship as a Waiting Game," Papers 91-3, Michigan - Center for Research on Economic & Social Theory.
  3. Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Social Choice: A Mean Voter Theorem," Econometrica, Econometric Society, vol. 59(1), pages 1-23, January.
  4. Laffont, Jean-Jacques & Tirole, Jean, 1988. "The Dynamics of Incentive Contracts," Econometrica, Econometric Society, vol. 56(5), pages 1153-75, September.
  5. Andrew Caplin & Barry Nalebuff, 1990. "Aggregation and Imperfect Competition: On the Existence of Equilibrium," Cowles Foundation Discussion Papers 937, Cowles Foundation for Research in Economics, Yale University.
  6. Christopher J. Flinn & James J. Heckman, 1982. "Are Unemployment and Out of the Labor Force Behaviorally Distinct Labor Force States?," NBER Working Papers 0979, National Bureau of Economic Research, Inc.
  7. Burdett, Kenneth, 1996. "Truncated means and variances," Economics Letters, Elsevier, vol. 52(3), pages 263-267, September.
  8. 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.
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