Extreme behaviour for bivariate elliptical distributions

Belkacem Abdous · Anne‐Laure Fougères · Kilani Ghoudi

53 citations0/0 files storedCanadian Journal of Statistics

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Probability and Risk Models Probability and Statistical Research Statistical Distribution Estimation and Applications

Abstract

The authors examine the asymptotic behaviour of conditional threshold exceedance probabilities for an elliptically distributed pair (X, Y) of random variables. More precisely, they investigate the limiting behaviour of the conditional distribution of Y given that X becomes extreme. They show that this behaviour differs between regularly and rapidly varying tails.

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References

1999Coherent Measures of Risk 1987Extreme Values, Regular Variation and Point Processes 2002Correlation and Dependence in Risk Management: Properties and Pitfalls 1989A Moment Estimator for the Index of an Extreme-Value Distribution 2004A Conditional Approach for Multivariate Extreme Values (with Discussion)2001Tail-Index Estimates in Small Samples 1998Selecting the optimal sample fraction in univariate extreme value estimation 2002Multivariate extremes, aggregation and dependence in elliptical distributions

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2019Extremal dependence of random scale constructions 2008Tail dependence of skewed grouped t -distributions

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