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. Estimation in certain parametric EV submodels will be investigated.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Joe, H. (1993). Parametric families of multivariate distributions with given marginals. J. Mult. Analysis 46, 262–282.
McFadden, D. (1978). Modelling the choice of residential location. In: Spatial Interaction Theory and Planning Models, pp.75–96, A. Karlquist et al. (eds.), North Holland, Amsterdam.
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 $E(k) by survivor functions (cf. (7.3)), one obtains the original representation.
For supplementary material concerning multivariate EV models see [12] and Tiago de Oliveira, J. (1989). Statistical decisions for bivariate extremes. In [10], pp. 246–261.
Smith, R.L., Tawn, J.A. and Yuen, H.K. (1990). Statistics of multivariate extremes. ISI Review 58, 47–58.
Csörgö, S. and Welsh, A.H. (1989). Testing for exponential and Marshall—Olkin distributions. J. Statist. Plan. Inference 23, 287–300.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer Basel AG
About this chapter
Cite this chapter
Reiss, RD., Thomas, M. (1997). Multivariate Maxima. In: Statistical Analysis of Extreme Values. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6336-0_8
Download citation
DOI: https://doi.org/10.1007/978-3-0348-6336-0_8
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-5768-9
Online ISBN: 978-3-0348-6336-0
eBook Packages: Springer Book Archive