Lp-metric under the location-independent risk ordering of random variables

Jianping Yang, Weiwei Zhuang and Taizhong Hu

Insurance: Mathematics and Economics, 2014, vol. 59, issue C, 321-324

Abstract: The Lp-metric Δh,p(X) between the survival function F¯ of a random variable X and its distortion h∘F¯ is a characteristic of the variability of X. In this paper, it is shown that if a random variable X is larger than another random variable Y in the location-independent risk order or in the excess wealth order, then Δh,p(X)≥Δh,p(Y) whenever p∈(0,1] and the distortion function h is convex or concave. An alternative and simple proof of the corresponding known result in the literature for the dispersive order is given. Some applications are also presented.

Keywords: Distortion function; The excess wealth order; The location-independent risk order; Order statistics; Variability (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:59:y:2014:i:c:p:321-324

DOI: 10.1016/j.insmatheco.2014.10.009

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