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