- References
A distortion function 
is a non-decreasing function such that 
and 
. The dual distortion function is 
.[1][2] Distortion functions are used to define distortion risk measures.[2]
Given a probability space 
, then for any random variable 
and any distortion function 
we can define a new probability measure 
such that for any 
it follows that
[1]
References
1. ^1 {{Cite journal | last1 = Balbás | first1 = A. | last2 = Garrido | first2 = J. | last3 = Mayoral | first3 = S. | doi = 10.1007/s11009-008-9089-z | title = Properties of Distortion Risk Measures | journal = Methodology and Computing in Applied Probability | volume = 11 | issue = 3 | pages = 385 | year = 2008 | pmid = | pmc = }}
2. ^1 {{cite web|title=Distortion Risk Measures: Coherence and Stochastic Dominance|author=Julia L. Wirch|author2=Mary R. Hardy|url=http://pascal.iseg.utl.pt/~cemapre/ime2002/main_page/papers/JuliaWirch.pdf|accessdate=March 10, 2012}}
{{probability-stub}}2. ^1 {{cite web|title=Distortion Risk Measures: Coherence and Stochastic Dominance|author=Julia L. Wirch|author2=Mary R. Hardy|url=http://pascal.iseg.utl.pt/~cemapre/ime2002/main_page/papers/JuliaWirch.pdf|accessdate=March 10, 2012}}
1 : Functions related to probability distributions