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Log-concave distributions: definitions, properties, and consequences

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If you have a question about this talk, please contact Richard Samworth.

In this talk I will review some results concerning log-concave distributions on one and higher dimensional Euclidean spaces, with emphasis on preservation results, strong log-concavity for both discrete and continuous distributions, and connections with questions arising from statistics.

I will sketch a proof of the log-concavity of Chernoff’s distribution, and briefly mention further problems.

Some background material for this talk is given in the book ‘Unimodality, Convexity and Applications’ by S. Dharmadhikari and K. Joag-dev, Academic Press, 1988.

This talk is part of the Statistics series.

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