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New developments on the Lp-metric between a probability distribution and its distortion

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  • Yang, Jianping
  • Hu, Taizhong

Abstract

Let Δh,p(X) denote the Lp-metric between the survival function F¯ of a random variable X and its distortion h∘F¯. It is shown that if X is smaller than Y in the convex order, then Δh,p(X)≤Δh,p(Y) whenever p∈(0,1] and the distortion function h is convex or concave. The corresponding results for some other stochastic orders are also presented.

Suggested Citation

  • Yang, Jianping & Hu, Taizhong, 2016. "New developments on the Lp-metric between a probability distribution and its distortion," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 236-243.
    • Handle: RePEc:eee:stapro:v:110:y:2016:i:c:p:236-243
    DOI: 10.1016/j.spl.2015.10.006
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    References listed on IDEAS

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    1. Ian Jewitt, 1989. "Choosing Between Risky Prospects: The Characterization of Comparative Statics Results, and Location Independent Risk," Management Science, INFORMS, vol. 35(1), pages 60-70, January.
    2. Muller, Alfred, 1996. "Orderings of risks: A comparative study via stop-loss transforms," Insurance: Mathematics and Economics, Elsevier, vol. 17(3), pages 215-222, April.
    3. Wang, Shaun, 1996. "Premium Calculation by Transforming the Layer Premium Density," ASTIN Bulletin, Cambridge University Press, vol. 26(1), pages 71-92, May.
    4. Muller, Alfred, 1998. "Comparing risks with unbounded distributions," Journal of Mathematical Economics, Elsevier, vol. 30(2), pages 229-239, September.
    5. López-Díaz, Miguel & Sordo, Miguel A. & Suárez-Llorens, Alfonso, 2012. "On the Lp-metric between a probability distribution and its distortion," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 257-264.
    6. Wang, Shaun S. & Young, Virginia R., 1998. "Ordering risks: Expected utility theory versus Yaari's dual theory of risk," Insurance: Mathematics and Economics, Elsevier, vol. 22(2), pages 145-161, June.
    7. Yang, Jianping & Zhuang, Weiwei & Hu, Taizhong, 2014. "Lp-metric under the location-independent risk ordering of random variables," Insurance: Mathematics and Economics, Elsevier, vol. 59(C), pages 321-324.
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    Cited by:

    1. Hu, Taizhong & Chen, Ouxiang, 2020. "On a family of coherent measures of variability," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 173-182.

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