# Distortion function

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{{Technical|date=November 2021}}
A '''distortion function''' in [mathematics](/source/mathematics) and [statistics](/source/statistics), for example, <math>g: [0,1] \to [0,1]</math>, is a [non-decreasing function](/source/non-decreasing_function) such that <math>g(0) = 0</math> and <math>g(1) = 1</math>.  The '''dual distortion function''' is <math>\tilde{g}(x) = 1 - g(1-x)</math>.<ref name="PropertiesDRM">{{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 | hdl = 10016/14071 | s2cid = 53327887 | hdl-access = free }}</ref><ref name="Wirch">{{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|access-date=March 10, 2012|archive-url=https://web.archive.org/web/20160705041252/http://pascal.iseg.utl.pt/~cemapre/ime2002/main_page/papers/JuliaWirch.pdf|archive-date=July 5, 2016|url-status=dead}}</ref>  Distortion functions are used to define [distortion risk measure](/source/distortion_risk_measure)s.<ref name="Wirch"/>

== References ==
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Category:Functions related to probability distributions

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Adapted from the Wikipedia article [Distortion function](https://en.wikipedia.org/wiki/Distortion_function) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Distortion_function?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.