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→Log-concave distributions: corrections about Wishart, also add Dirichlet |
→Log-concave distributions: fixes, explanation for parameter restrictions |
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*The [[chi distribution]].
*The [[Wishart distribution]], where ''n'' >= ''p'' + 1.<ref name="prekopa">András Prékopa (1971), "Logarithmic concave measures with application to stochastic programming". ''Acta Scientiarum Mathematicarum'', 32, pp. 301–316.</ref>
*The [[Dirichlet distribution]], where all parameters are >= 1.<ref name="prekopa"/>
*The [[gamma distribution]] if the shape parameter is >= 1.
*The [[chi-square distribution]] if the number of degrees of freedom is >= 2.
*The [[beta distribution]] if both shape parameters are >= 1.
*The [[Weibull distribution]] if the shape parameter is >= 1.
Note that all of the parameter restrictions have the same basic source: The exponent of non-negative quantity must be non-negative in order for the function to be log-concave.
The following distributions are non-log-concave for all parameters:
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