Logconcavity versus Logconvexity: A Complete Characterization

Mark Y An ()

No 95-03, Working Papers from Duke University, Department of Economics

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.

JEL-codes: D80 C12 C14 (search for similar items in EconPapers)
Date: 1995

Published in JOURNAL OF ECONOMIC THEORY, Vol. 80, 1998, pages 350-369

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Journal Article: Logconcavity versus Logconvexity: A Complete Characterization (1998)
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