Distortion function

A distortion function in mathematics and statistics, for example, $g : [0, 1] \to [0, 1]$ , is a non-decreasing function such that $g (0) = 0$ and $g (1) = 1$ . The dual distortion function is $\tilde{g} (x) = 1 - g (1 - x)$ .^[1]^[2] Distortion functions are used to define distortion risk measures.^[2]

References

↑ 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.
1 2 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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[PropertiesDRM-1] 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.

[Wirch-2] 1 2 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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