Modelling extremal data

ABSTRACT

We consider large and small sample modelling of extreme value data. For large sample sizes, we introduce big new subclasses of the domains of attraction of the Gumbel, Fréchet, and Weibull extreme value limits laws and determine the corresponding sequences of centring and normalizing constants. In the case of small sample sizes, we compare dependence modelling of maxima in multivariate $l_{n,p}$-symmetric sample distributions with two types of independence modelling. For this purpose, we use, on the one hand, independent $l_{1,p}$-symmetrically distributed random variables and, on the other hand, independent random variables being univariate marginals of $l_{k,p}$-symmetrically distributed vectors. In the latter case, we first demonstrate the influence of k, and finally indicate one of its values showing the model being the closest to the dependence model.

KEYWORDS:

• Density generator
• extreme value distributions
• $l_{n,p}$-dependency
• $l_{n,p}$-symmetric distributions
• sample size planning
• univariate marginal density generator

AMS SUBJECT CLASSIFICATION:

• 60G70
• 62E15
• 62E20
• 62G32

Acknowledgments

The authors are grateful to a reviewer for giving valuable hints which lead to improvements in presentation and structure of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.