On the Lp-metric between a probability distribution and its distortion

Miguel López-Díaz, Miguel A. Sordo and Alfonso Suárez-Llorens

Insurance: Mathematics and Economics, 2012, vol. 51, issue 2, 257-264

Abstract: In actuarial theory, the Lp-metric is used to evaluate how well a probability distribution approximates another one. In the context of the distorted expectation hypothesis, the actuary replaces the original probability distribution by a distorted probability, so it makes sense to interpret the Lp-metric between them as a characteristic of the underlying random variable. We show in this paper that this is a characteristic of the variability of the random variable, study its properties and give some applications.

Keywords: Metric; Distortion function; Variability measure; Dispersive order; Dilation order (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (11)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:51:y:2012:i:2:p:257-264

DOI: 10.1016/j.insmatheco.2012.04.004

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