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Tolerance intervals for quantiles of bivariate risks and risk measurement

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  • Gebizlioglu, Omer L.
  • Yagci, Banu

Abstract

This paper considers joint distributions of order statistics for risk variables and their concomitants for actuarial risk analysis under dependence. With this purpose, bivariate integral transformations are performed and some examples are presented using copulas, the FGM copulas in particular. Quantiles of the distributions concerned are discussed and their tolerance intervals are constructed. Risk measures such as VaR in the set up of the tolerance intervals are included in the discussions.

Suggested Citation

  • Gebizlioglu, Omer L. & Yagci, Banu, 2008. "Tolerance intervals for quantiles of bivariate risks and risk measurement," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1022-1027, June.
    • Handle: RePEc:eee:insuma:v:42:y:2008:i:3:p:1022-1027
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    References listed on IDEAS

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    1. I. Bairamov & S. Kotz & M. Bekci, 2001. "New generalized Farlie-Gumbel-Morgenstern distributions and concomitants of order statistics," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(5), pages 521-536.
    2. Chen, L. -A. & Welsh, A. H., 2002. "Distribution-Function-Based Bivariate Quantiles," Journal of Multivariate Analysis, Elsevier, vol. 83(1), pages 208-231, October.
    3. Rodríguez-Lallena, José A. & Úbeda-Flores, Manuel, 2003. "Distribution functions of multivariate copulas," Statistics & Probability Letters, Elsevier, vol. 64(1), pages 41-50, August.
    4. Nelsen, Roger B. & Quesada-Molina, José Juan & Rodríguez-Lallena, José Antonio & Úbeda-Flores, Manuel, 2001. "Distribution functions of copulas: a class of bivariate probability integral transforms," Statistics & Probability Letters, Elsevier, vol. 54(3), pages 277-282, October.
    5. Tank, Fatih & Gebizlioglu, Omer L. & Apaydin, Aysen, 2006. "Determination of dependency parameter in joint distribution of dependent risks by fuzzy approach," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 189-194, February.
    6. Denuit, M. & Genest, C. & Marceau, E., 1999. "Stochastic bounds on sums of dependent risks," Insurance: Mathematics and Economics, Elsevier, vol. 25(1), pages 85-104, September.
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    Cited by:

    1. Buch-Kromann, Tine & Guillén, Montserrat & Linton, Oliver & Nielsen, Jens Perch, 2011. "Multivariate density estimation using dimension reducing information and tail flattening transformations," Insurance: Mathematics and Economics, Elsevier, vol. 48(1), pages 99-110, January.
    2. Pitselis, Georgios, 2013. "Quantile credibility models," Insurance: Mathematics and Economics, Elsevier, vol. 52(3), pages 477-489.
    3. Fernández, Arturo J., 2010. "Two-sided tolerance intervals in the exponential case: Corrigenda and generalizations," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 151-162, January.
    4. Pitselis, Georgios, 2020. "Multi-stage nested classification credibility quantile regression model," Insurance: Mathematics and Economics, Elsevier, vol. 92(C), pages 162-176.

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