2 results about "Distortion function" patented technology

A distortion function g:[0,1]→[0,1] is a non-decreasing function such that g(0)=0 and g(1)=1. The dual distortion function is g(x)=1-g(1-x). Distortion functions are used to define distortion risk measures. Given a probability space (Ω,F,ℙ), then for any random variable X and any distortion function g we can define a new probability measure ℚ such that for any A∈F it follows that ℚ(A)=g(ℙ(X∈A)).