A distortion function in mathematics and statistics, for example, formula_1, is a non-decreasing function such that formula_2 and formula_3. The dual distortion function is formula_4. Distortion functions are used to define distortion risk measures.
Given a probability space formula_5, then for any random variable formula_6 and any distortion function formula_7 we can define a new probability measure formula_8 such that for any formula_9 it follows that
 formula_10 
References.
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