Distortion function

A distortion function in mathematics and statistics, for example, ${\displaystyle g:[0,1]\to [0,1]}$, is a non-decreasing function such that ${\displaystyle g(0)=0}$ and ${\displaystyle g(1)=1}$. The dual distortion function is ${\displaystyle {\tilde {g}}(x)=1-g(1-x)}$.^[1][2] Distortion functions are used to define distortion risk measures.^[2]