Revision as of 17:18, 2 June 2016 edit Aby.vinod (talk \| contribs) 21 edits Explained why it is a fact along with reference. Tag: Visual edit ← Previous edit		Revision as of 17:20, 2 June 2016 edit undo Aby.vinod (talk \| contribs) 21 edits →Properties Next edit →
Line 18: ==Properties== * A log-concave function is also [[Quasi-concave function\|quasi-concave]]. This follows from the fact that the logarithm is monotone implying that the superlevel sets of this function are ~~concave~~convex.<ref name=":0" /> * Every concave function that is nonnegative on its ___domain is log-concave. However, the reverse does not necessarily hold. An example is the [[Gaussian function]] {{math\|''f''(''x'')}} = {{math\|exp(−x<sup>2</sup>/2)}} which is log-concave since {{math\|log ''f''(''x'')}} = {{math\|−''x''<sup>2</sup>/2}} is a concave function of {{math\|''x''}}. But {{math\|''f''}} is not concave since the second derivative is positive for \|{{math\|''x''}}\| > 1:

Logarithmically concave function: Difference between revisions