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TAIL CONDITIONAL EXPECTATIONS FOR GENERALIZED SKEW-ELLIPTICAL DISTRIBUTIONS

Published online by Cambridge University Press:  05 January 2021

Baishuai Zuo Open the ORCID record for Baishuai Zuo [Opens in a new window]  and
Chuancun Yin
Baishuai Zuo
Affiliation:
School of Statistics, Qufu Normal University, Qufu, Shandong273165, P. R. China E-mail: ccyin@qfnu.edu.cn
Chuancun Yin
Affiliation:
School of Statistics, Qufu Normal University, Qufu, Shandong273165, P. R. China E-mail: ccyin@qfnu.edu.cn
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Abstract

This paper deals with the multivariate tail conditional expectation (MTCE) for generalized skew-elliptical distributions. We present tail conditional expectation for univariate generalized skew-elliptical distributions and MTCE for generalized skew-elliptical distributions. There are many special cases for generalized skew-elliptical distributions, such as generalized skew-normal, generalized skew Student-t, generalized skew-logistic and generalized skew-Laplace distributions.

Keywords

generalized skew-elliptical distributionsgeneralized skew-Laplacegeneralized skew-logisticgeneralized skew Student-tmultivariate risk measurestail conditional expectations
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 36 , Issue 2 , April 2022 , pp. 500 - 513
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press

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References

Adcock, C., Landsman, Z., & Shushi, T. (2019). Stein's lemma for generalized skew-elliptical random vectors. Communications in Statistics-Theory and Methods: 1–16. doi:10.1080/03610926.2019.1678642Google Scholar
Fang, K.T., Kotz, S., & Ng, K.W. (1990). Symmetric multivariate and related distributions. New York: Chapman and Hall.CrossRefGoogle Scholar
Ignatieva, K. & Landsman, Z. (2015). Estimating the tail of loss severity via conditional risk measures for the family of symmetric generalised hyperbolic distributions. Insurance: Mathematics and Economics 65: 172–186.Google Scholar
Ignatieva, K. & Landsman, Z. (2019). Conditional tail risk measures for the skewed generalised hyperbolic family. Insurance: Mathematics and Economics 86: 98–114.Google Scholar
Kim, J.H.T. (2010). Conditional tail moments of the exponential family and its related distributions. North American Actuarial Journal 14: 198–216.Google Scholar
Landsman, Z., Makov, U., & Shushi, T. (2016). Multivariate tail conditional expectation for elliptical distributions. Insurance: Mathematics and Economics 70: 216–223.Google Scholar
Landsman, Z., Makov, U., & Shushi, T. (2018). A multivariate tail covariance measure for elliptical distributions. Insurance: Mathematics and Economics 81: 27–35.Google Scholar
Landsman, Z. & Nešlehová, J. (2008). Stein's Lemma for elliptical random vectors. Journal of Multivariate Analysis 99: 912–927.CrossRefGoogle Scholar
Landsman, Z.M. & Valdez, E.A. (2003). Tail conditional expectations for elliptical distributions. North American Actuarial Journal 7: 55–71.CrossRefGoogle Scholar
Lin, S.D., Srivastava, H.M., & Wang, P.Y. (2006). Some expansion formulas for a class of generalized Hurwitz-Lerch Zeta functions. Integral Transforms and Special Functions 17(11): 817–827.CrossRefGoogle Scholar
Mousavi, S.A., Amirzadeh, V., Rezapour, M., & Sheikhy, A. (2019). Multivariate tail conditional expectation for scale mixtures of skew-normal distribution. Journal of Statistical Computation and Simulation: 1–15. doi:10.1080/00949655.2019.1657864Google Scholar
Panjer, H.H. (2002). Measurement of risk, solvency requirements, and allocation of capital within financial conglomerates. Institute of Insurance and Pension Research, University of Waterloo, Research Report, 01–15.Google Scholar