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A distortion function in mathematics and statistics, for example, g : → {\displaystyle g:\to } , is a non-decreasing function such that g = 0 {\displaystyle g=0} and g = 1 {\displaystyle g=1}. The dual distortion function is g ~ = 1 − g {\displaystyle {\tilde {g}}=1-g}. Distortion functions are used to define distortion risk measures.
Given a probability space {\displaystyle } , then for any random variable X {\displaystyle X} and any distortion function g {\displaystyle g} we can define a new probability measure Q {\displaystyle \mathbb {Q} } such that for any A ∈ F {\displaystyle A\in {\mathcal {F}}} it follows that