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Extremal properties of the skew-t distribution

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  • Peng, Zuoxiang
  • Li, Chunqiao
  • Nadarajah, Saralees

Abstract

Asymptotic behaviors of the extremes of the skew-t distribution are derived. The study is two folded. The first states the norming constant for the limiting distribution of the sample partial maximum for the skew-t distribution. The second establishes higher order expansions of the probability density and cumulative distribution functions for the maximum under a suitable norming constant.

Suggested Citation

  • Peng, Zuoxiang & Li, Chunqiao & Nadarajah, Saralees, 2016. "Extremal properties of the skew-t distribution," Statistics & Probability Letters, Elsevier, vol. 112(C), pages 10-19.
    • Handle: RePEc:eee:stapro:v:112:y:2016:i:c:p:10-19
    DOI: 10.1016/j.spl.2016.01.017
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    References listed on IDEAS

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    1. Fung, Thomas & Seneta, Eugene, 2014. "Convergence rate to a lower tail dependence coefficient of a skew-t distribution," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 62-72.
    2. Padoan, Simone A., 2011. "Multivariate extreme models based on underlying skew-t and skew-normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 102(5), pages 977-991, May.
    3. Liao, Xin & Peng, Zuoxiang & Nadarajah, Saralees, 2013. "Asymptotic expansions for moments of skew-normal extremes," Statistics & Probability Letters, Elsevier, vol. 83(5), pages 1321-1329.
    4. Saralees Nadarajah & Emmanuel Afuecheta & Stephen Chan, 2015. "GARCH modeling of five popular commodities," Empirical Economics, Springer, vol. 48(4), pages 1691-1712, June.
    5. Bernardi, Mauro & Maruotti, Antonello & Petrella, Lea, 2012. "Skew mixture models for loss distributions: A Bayesian approach," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 617-623.
    6. Eling, Martin, 2012. "Fitting insurance claims to skewed distributions: Are the skew-normal and skew-student good models?," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 239-248.
    7. Adelchi Azzalini & Marc G. Genton, 2008. "Robust Likelihood Methods Based on the Skew‐t and Related Distributions," International Statistical Review, International Statistical Institute, vol. 76(1), pages 106-129, April.
    8. Lysenko, Natalia & Roy, Parthanil & Waeber, Rolf, 2009. "Multivariate extremes of generalized skew-normal distributions," Statistics & Probability Letters, Elsevier, vol. 79(4), pages 525-533, February.
    9. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
    10. Jeffrey Chu & Saralees Nadarajah & Stephen Chan, 2015. "Statistical Analysis of the Exchange Rate of Bitcoin," PLOS ONE, Public Library of Science, vol. 10(7), pages 1-27, July.
    11. Vernic, Raluca, 2006. "Multivariate skew-normal distributions with applications in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 38(2), pages 413-426, April.
    12. Saralees Nadarajah & Emmanuel Afuecheta & Stephen Chan, 2015. "A note on "Modelling exchange rate returns: which flexible distribution to use?"," Quantitative Finance, Taylor & Francis Journals, vol. 15(11), pages 1777-1785, November.
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    2. Beranger, B. & Padoan, S.A. & Xu, Y. & Sisson, S.A., 2019. "Extremal properties of the multivariate extended skew-normal distribution, Part B," Statistics & Probability Letters, Elsevier, vol. 147(C), pages 105-114.

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