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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

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 80 (1998)
Issue (Month): 2 (June)
Pages: 350-369

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Handle: RePEc:eee:jetheo:v:80:y:1998:i:2:p:350-369

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Web page: http://www.elsevier.com/locate/inca/622869

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  1. Jean-Jacques Laffont & Jean Tirole, 1985. "The Dynamics of Incentive Contracts," Working papers 397, Massachusetts Institute of Technology (MIT), 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. 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.
  4. Heckman, James J & Honore, Bo E, 1990. "The Empirical Content of the Roy Model," Econometrica, Econometric Society, vol. 58(5), pages 1121-49, September.
  5. Bergstrom, T. & Bagnoli, M., 1991. "Courtship as a waiting game," The Warwick Economics Research Paper Series (TWERPS) 386, University of Warwick, Department of Economics.
  6. Caplin, A. & Nalebuff, B., 1989. "Aggregation And Social Choice: A Mean Voter Theorem," Discussion Papers 1989_31, Columbia University, Department of Economics.
  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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