Logarithmically concave function: Difference between revisions

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==Log-concave distributions==

Log-concave distributions are necessary for a number of algorithms, e.g. [[adaptive rejection sampling]]. Every distribution with log-concave density is a maximal[[maximum entropy probability distribution]] with specified mean ''μ'' and [[Deviation risk measure]] ''D'' <ref name="Grechuk1">Grechuk, B., Molyboha, A., Zabarankin, M. (2009) [https://www.researchgate.net/publication/220442393_Maximum_Entropy_Principle_with_General_Deviation_Measures Maximum Entropy Principle with General Deviation Measures], Mathematics of Operations Research 34(2), 445--467, 2009.</ref>.

As it happens, many common [[probability distribution]]s are log-concave. Some examples:<ref>See Mark Bagnoli and Ted Bergstrom (1989), "Log-Concave Probability and Its Applications", University of Michigan.[http://www.econ.ucsb.edu/~tedb/Theory/delta.pdf]</ref>

*The [[normal distribution]] and [[multivariate normal distribution]]s.