Jensen's Inequality For Medians
Jensen's inequality states that for any random variable x with a finite expectation E(X) and for any convex function f then
It has been shown that if x is a real variable with a unique median m and f is a C function then
A C function is a real valued function, defined on the set of real numbers R, with the property that for any real t
is a closed interval, a singleton or an empty set.
Read more about this topic: Median
Famous quotes containing the word inequality:
“All the aspects of this desert are beautiful, whether you behold it in fair weather or foul, or when the sun is just breaking out after a storm, and shining on its moist surface in the distance, it is so white, and pure, and level, and each slight inequality and track is so distinctly revealed; and when your eyes slide off this, they fall on the ocean.”
—Henry David Thoreau (1817–1862)