Abstract
Multivariate extreme value (EV) distributions are introduced as limiting distributions of componentwise taken maxima. In contrast to the univariate case, the resulting statistical model is a nonparametric one. Some basic properties and first examples of multivariate EV dfs are dealt with in Section 12.1.
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References
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Such a representation is given in Joe, H. (1994). Multivariate extreme-value distributions with applications to environmental data. Canad. J. Statist. 22, 47–64. Replacing ΦΣ(k) by survivor functions (cf. (10.4)), one obtains the original representation.
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For supplementary results concerning multivariate EV models see [16] and Tiago de Oliveira, J. (1989). Statistical decisions for bivariate extremes. In [14], pp. 246–261, or Smith, R.L., Tawn, J.A. and Yuen, H.K. (1990). Statistics of multivariate extremes. ISI Review 58, 47–58.
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(2007). Multivariate Maxima. In: Statistical Analysis of Extreme Values. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7399-3_12
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DOI: https://doi.org/10.1007/978-3-7643-7399-3_12
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-7230-9
Online ISBN: 978-3-7643-7399-3
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