Distortion function

A distortion function in mathematics and statistics, for example, $g:[0,1]\to [0,1]$, is a non-decreasing function such that $g(0)=0$ and $g(1)=1$. The dual distortion function is $\tilde{g}(x)=1-g(1-x)$. Distortion functions are used to define distortion risk measures.