Distortion function
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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A distortion function in mathematics and statistics, for example, , 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]
![{\displaystyle g:[0,1]\to [0,1]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/0329691aecddec5158ad537f5df2e83578a302e2)
References
[edit]- ^ Balbás, A.; Garrido, J.; Mayoral, S. (2008). "Properties of Distortion Risk Measures". Methodology and Computing in Applied Probability. 11 (3): 385. doi:10.1007/s11009-008-9089-z. hdl:10016/14071. S2CID 53327887.
- ^ a b Julia L. Wirch; Mary R. Hardy. "Distortion Risk Measures: Coherence and Stochastic Dominance" (PDF). Archived from the original (PDF) on July 5, 2016. Retrieved March 10, 2012.
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