Logarithmically concave function: Difference between revisions

Revision as of 17:20, 2 June 2016

Revision as of 16:32, 20 June 2016

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::<math>f''(x)=e^{-\frac{x^2}{2}} (x^2-1) \nleq 0</math>

* From above two points, [[Concave_function|concavity]] <math>\Rightarrow</math> log-concavity <math>\Rightarrow</math> [[Quasiconcave_function|quasiconcavity]].

* A twice differentiable, nonnegative function with a convex ___domain is log-concave if and only if for all {{math|''x''}} satisfying {{math|''f''(''x'')&nbsp;>&nbsp;0}},