Some subclasses of elliptical distributions

1990 ◽  
pp. 69-95
Author(s):  
Kai-Tai Fang ◽  
Samuel Kotz ◽  
Kai Wang Ng
Keyword(s):  
Elliptical Distributions

A note on the generalization of bivariate normal quadrant probabilities to bivariate elliptical distributions

2018 ◽  
Author(s):  
Oscar Lorenzo Olvera Astivia
Keyword(s):  
Normal Distribution ◽  
Bivariate Normal Distribution ◽  
Elliptical Distributions ◽  
Bivariate Normal ◽  
Geometric Argument

I present a geometric argument to show that the quadrant probability for the bivariate normal distribution can be generalized to the case of all elliptical distributions.

Inference for Vast Dimensional Elliptical Distributions

2012 ◽  
Author(s):  
Yves Dominicy ◽  
Hiroaki Ogata ◽  
David Veredas
Keyword(s):  
Elliptical Distributions

scholarly journals Multivariate Tail Moments for Log-Elliptical Dependence Structures as Measures of Risks

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 559
Author(s):  
Zinoviy Landsman ◽  
Tomer Shushi
Keyword(s):  
Risk Measures ◽  
Short Paper ◽  
Dependence Structure ◽  
Elliptical Distributions ◽  
Tail Conditional Expectation ◽  
Special Cases ◽  
Optimal Portfolio Selection ◽  
Multivariate Risk Measures ◽  
Elliptical Models ◽  
Risk Managers

The class of log-elliptical distributions is well used and studied in risk measurement and actuarial science. The reason is that risks are often skewed and positive when they describe pure risks, i.e., risks in which there is no possibility of profit. In practice, risk managers confront a system of mutually dependent risks, not only one risk. Thus, it is important to measure risks while capturing their dependence structure. In this short paper, we compute the multivariate risk measures, multivariate tail conditional expectation, and multivariate tail covariance measure for the family of log-elliptical distributions, which captures the dependence structure of the risks while focusing on the tail of their distributions, i.e., on extreme loss events. We then study our result and examine special cases, as well as the optimal portfolio selection using such measures. Finally, we show how the given multivariate tail moments can also be computed for log-skew elliptical models based on similar approaches given for the log-elliptical case.

Multivariate extremes, aggregation and dependence in elliptical distributions

2002 ◽  
Vol 34 (03) ◽  
pp. 587-608 ◽  
Author(s):  
Henrik Hult ◽  
Filip Lindskog
Keyword(s):  
Random Vector ◽  
Positive Constant ◽  
Tail Dependence ◽  
Constant Factor ◽  
Dispersion Matrix ◽  
Elliptical Distributions ◽  
Spectral Measures ◽  
Lower Tail ◽  
Explicit Formulae ◽  
Dependence Properties

In this paper, we clarify dependence properties of elliptical distributions by deriving general but explicit formulae for the coefficients of upper and lower tail dependence and spectral measures with respect to different norms. We show that an elliptically distributed random vector is regularly varying if and only if the bivariate marginal distributions have tail dependence. Furthermore, the tail dependence coefficients are fully determined by the tail index of the random vector (or equivalently of its components) and the linear correlation coefficient. Whereas Kendall's tau is invariant in the class of elliptical distributions with continuous marginals and a fixed dispersion matrix, we show that this is not true for Spearman's rho. We also show that sums of elliptically distributed random vectors with the same dispersion matrix (up to a positive constant factor) remain elliptical if they are dependent only through their radial parts.

Smooth Monotone Covariance for Elliptical Distributions and Applications in Finance

2014 ◽  
Author(s):  
Xiaoping Zhou ◽  
Dmitry Malioutov ◽  
Frank J. Fabozzi ◽  
Svetlozar Rachev
Keyword(s):  
Elliptical Distributions

A Bayesian Framework for Estimating the Concordance Correlation Coefficient Using Skew-elliptical Distributions

2018 ◽  
Vol 14 (1) ◽  
Author(s):  
Dai Feng ◽  
Richard Baumgartner ◽  
Vladimir Svetnik
Keyword(s):  
Clinical Study ◽  
Missing Data ◽  
Correlation Coefficient ◽  
Real Life ◽  
Bayesian Framework ◽  
Concordance Correlation Coefficient ◽  
Elliptical Distributions ◽  
Concordance Correlation ◽  
Heavy Tailed ◽  
Biomarker Data

Abstract The concordance correlation coefficient (CCC) is a widely used scaled index in the study of agreement. In this article, we propose estimating the CCC by a unified Bayesian framework that can (1) accommodate symmetric or asymmetric and light- or heavy-tailed data; (2) select model from several candidates; and (3) address other issues frequently encountered in practice such as confounding covariates and missing data. The performance of the proposal was studied and demonstrated using simulated as well as real-life biomarker data from a clinical study of an insomnia drug. The implementation of the proposal is accessible through a package in the Comprehensive R Archive Network.

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