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Assessing the difference between integrated quantiles and integrated cumulative distribution functions

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  • Yunran Wei
  • Ricardas Zitikis

Abstract

This paper offers a mathematical invention that shows how to convert integrated quantiles, which often appear in risk measures, into integrated cumulative distribution functions, which are technically more tractable from various perspectives. The invention helps to avoid a number of technical assumptions that have been traditionally imposed when working with quantities containing quantiles. In particular it helps to completely avoid the requirement of the existence of a probability density function. The developed results explain and illustrate the invention, whose byproducts include the assessment of model uncertainty and misspecification, and the derivation of statistical inference results.

Suggested Citation

  • Yunran Wei & Ricardas Zitikis, 2022. "Assessing the difference between integrated quantiles and integrated cumulative distribution functions," Papers 2210.16880, arXiv.org, revised Apr 2023.
    • Handle: RePEc:arx:papers:2210.16880
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    File URL: http://arxiv.org/pdf/2210.16880
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    References listed on IDEAS

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    1. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496.
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    7. Bellini, Fabio & Fadina, Tolulope & Wang, Ruodu & Wei, Yunran, 2022. "Parametric measures of variability induced by risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 270-284.
    8. Fabio Bellini & Tolulope Fadina & Ruodu Wang & Yunran Wei, 2020. "Parametric measures of variability induced by risk measures," Papers 2012.05219, arXiv.org, revised Apr 2022.
    9. Peng, Liang & Qi, Yongcheng & Wang, Ruodu & Yang, Jingping, 2012. "Jackknife empirical likelihood method for some risk measures and related quantities," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 142-150.
    10. Abdelhakim Necir & Abdelaziz Rassoul & Ričardas Zitikis, 2010. "Estimating the Conditional Tail Expectation in the Case of Heavy-Tailed Losses," Journal of Probability and Statistics, Hindawi, vol. 2010, pages 1-17, April.
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    Cited by:

    1. N. V. Gribkova & J. Su & R. Zitikis, 2024. "Assessing the coverage probabilities of fixed-margin confidence intervals for the tail conditional allocation," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 76(5), pages 821-850, October.

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