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Estimation of the tail exponent of multivariate regular variation

Annals of the Institute of Statistical Mathematics, 2016
It is well known that the extreme behavior of multivariate observations can be characterized by a spectral measure and a tail exponent. The estimation of this latter quantity is considered here, which is grounded on the fact that every convex combination of a random vector having a multivariate regularly varying tail also has a univariate regularly ...
Kim, Moosup, Lee, Sangyeol
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Multivariate Regular Variation in Probability Theory

Journal of Mathematical Sciences, 2020
This paper provides a brief overview of various definitions of multivariate regularly varying functions and some of their applications in probability theory and related fields.
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First and Second Order Asymptotics of the Spectral Risk Measure for Portfolio Loss Under Multivariate Regular Variation

Journal of Systems Science and Complexity, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Guo-Dong Xing, Shanchao Yang
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Multivariate Regular Variation and its Applications

2015
In this thesis, we review the basic notions related to univariate regular variation and study some fundamental properties of regularly varying random variables. We then consider the notion of regular variation in the multivariate case. After collecting some results from multivariate regular variation for random vectors with values in $\mathbb{R}_{+}^{d}
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