Logconcavity versus logconvexity: a complete characterization.
The writer presents a complete characterization of logconcavity, which is an increasingly popular concept in the economics of uncertainty and information. He points out that a random variable or a random vector is logconcavely distributed if the logarithm of its probability density function is conc...
| Published in: | Journal of Economic Theory Vol. 80; no. 2; pp. 350 - 370 |
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| Format: | Article |
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Academic Press Inc.
June 1998
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| Online Access: | View this record in EBSCOhost |
| Summary: | The writer presents a complete characterization of logconcavity, which is an increasingly popular concept in the economics of uncertainty and information. He points out that a random variable or a random vector is logconcavely distributed if the logarithm of its probability density function is concave. He proves new and known results without the assumption that density functions are differentiable. He undertakes a systematic comparison between logconcavity and logconvexity and explores the source of the asymmetries between the two. He points out that the key difference is that logconcavity is preserved under one-sided integrations regardless of the types of distribution supports. He notes that this property does not hold for logconvexity. In addition, he considers logconcavity for multivariate distributions. |
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