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Logconcavity versus Logconvexity: A Complete Characterization

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  • 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.

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Bibliographic Info

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
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Publication status: Published in JOURNAL OF ECONOMIC THEORY, Vol. 80, 1998, pages 350-369
Handle: RePEc:duk:dukeec:95-03

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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. Mark Bagnoli & Ted Bergstrom, . "Courtship as a Waiting Game," Papers _030, University of Michigan, Department of Economics.
  2. Caplin, A. & Nalebuff, B., 1989. "Aggregation And Imperfect Competition: On The Existence Of Equilibrium," Discussion Papers 1989_30, Columbia University, Department of Economics.
  3. Caplin, A. & Nalebuff, B., 1989. "Aggregation And Social Choice: A Mean Voter Theorem," Discussion Papers 1989_31, Columbia University, Department of Economics.
  4. Burdett, Kenneth, 1996. "Truncated means and variances," Economics Letters, Elsevier, vol. 52(3), pages 263-267, September.
  5. 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.
  6. Jean-Jacques Laffont & Jean Tirole, 1985. "The Dynamics of Incentive Contracts," Working papers 397, Massachusetts Institute of Technology (MIT), Department of Economics.
  7. 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.
  8. Heckman, James J & Honore, Bo E, 1990. "The Empirical Content of the Roy Model," Econometrica, Econometric Society, vol. 58(5), pages 1121-49, September.
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