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.
Length: 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
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Find related papers by JEL classification: D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Semiparametric and Nonparametric Methods
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