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:
“The doctrine of equality!... But there exists no more poisonous poison: for it seems to be preached by justice itself, while it is the end of justice.... “Equality for equals, inequality for unequals”Mthat would be the true voice of justice: and, what follows from it, “Never make equal what is unequal.””
—Friedrich Nietzsche (1844–1900)