Journal of Applied Probability

Weakening the independence assumption on polar components: limit theorems for generalized elliptical distributions

Miriam Isabel Seifert

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By considering the extreme behavior of bivariate random vectors with a polar representation R(u(T), v(T)), it is commonly assumed that the radial component R and the angular component T are stochastically independent. We investigate how to relax this rigid independence assumption such that conditional limit theorems can still be deduced. For this purpose, we introduce a novel measure for the dependence structure and present convenient criteria for validity of limit theorems possessing a geometrical meaning. Thus, our results verify a stability of the available limit results, which is essential in applications where the independence of the polar components is not necessarily present or exactly fulfilled.

Article information

J. Appl. Probab., Volume 53, Number 1 (2016), 130-145.

First available in Project Euclid: 8 March 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60F05: Central limit and other weak theorems
Secondary: 60G70: Extreme value theory; extremal processes 62E20: Asymptotic distribution theory 62G32: Statistics of extreme values; tail inference

Conditional extreme value model polar representation elliptical distribution Gumbel max-domain of attraction random norming


Seifert, Miriam Isabel. Weakening the independence assumption on polar components: limit theorems for generalized elliptical distributions. J. Appl. Probab. 53 (2016), no. 1, 130--145.

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