Schur-convex function: Difference between revisions

Revision as of 03:30, 20 September 2012

Revision as of 03:34, 20 September 2012

Line 26:

* Some probability examples: If <math> X_1, \dots, X_n </math> are exchangable random variables, then the function

:<math> \text{E} \prod_{j=1}^n X_j^{a_j} </math>
is Schur-convex as a function of <math> a=(a_1, \dots, a_n) </math>, assuming that the expectations exist.

* The [[Gini coefficient]] is strictly Schur convex.

==See also==

* [[majorization]]

* [[Quasiconvex function]]

* [[Convex function]]

[[Category:Convex analysis]]