The Meta-elliptical Distributions with Given Marginals

By Hong-Bin Fang, Kai-Tai Fang, Samuel Kotz. 2002

393 citations recorded by the source corpus.

Subfields: Finance, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/f96eb64ce5f2afcadf8943b5052e91de0dc17230

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Citations in the corpus

KENDALL'S TAU FOR ELLIPTICAL DISTRIBUTIONS ∗ (2003, methodology): “ a density. The extensions (3) and (4) are not given in [ 4 ].”
Copula-Based Models for Multivariate Discrete Response Data (2013, methodology): “Two well known members of elliptical copulas [7, 1], the MVN and Student t copulas have been used in the literature for prediction and modeling of dependent discrete data.”
Pair-copula constructions of multiple dependence (2009, methodology): “9 the empirical lambda function and its confidence bands, computed as described in Genest and Rivest (1993), are presented together with the fitted lambda functions for the Clayton copula and the Student copula.”
Multivariate drought characteristics using trivariate Gaussian and Student t copulas (2013, methodology): “The analytical expressions of trivariate Gaussian and Student t copulas are elaborately derived (see Appendix 2) based on some pioneering works (Kelly and Krzysztofowicz, 1997; Fang et al., 2002; Demarta and McNeil, 2005; Žežula, 2009).”
Analysis of elliptical copula correlation factor model with Kendall's tau (2013, background): “Standard factor analysis states that X = µ + LF + V 1 / 2 E , in distribution, for some mean vector µ ∈ R d , loading matrix L ∈ R d × r with r d , diagonal matrix V 1 / 2 ∈ R d × d and noise E ∈ R d , independent of random vector F = ( F 1 , . . . , F r ) T ∈ R r .”
Nonparametric inference on multivariate versions of Blomqvist’s beta and related measures of tail dependence (2007, background): “2 in Fang et al. (1990) - where the random variable R ≥ 0 is independent of the d-dimensional random vector U which is uniformly distributed on the unit sphere Sd−1 2 in R.”
Importance of Tail Dependence in Bivariate Frequency Analysis (2007, background): “…to address multivariate hydrological events as a generalization of univariate distributions, for instance, bivariate normal Goel et al. 1998 , bivariate lognormal Yue 2000 , bivariate exponential Favre et al. 2002 , bivariate gamma Yue et al. 2001 , or bivariate extreme value Adamson et al. 1999 .”
Stochastic frontier models with dependent error components (2008, methodology): “The joint PDF corresponds to a special case of the Meta-Gaussian distribution which is itself a special case of the Meta-Elliptical class of distributions (e.g. see Fang et al. 2002).”
Dynamic Copula Modelling for Value at Risk (2006, positive): “In this case we have the so-called meta joint distribution functions, whose theoretical background has been studied recently by Embrechts, Hoing, and Juri (2003) and Fang and Fang (2002).”
Goodness-of-Fit Tests for Copulas of Multivariate Time Series (2017, neutral): “In fact, τjk = τ(Uji, Uki) = 2 π arcsin(rjk) [42].”
Everything You Always Wanted to Know about Copula Modeling but Were Afraid to Ask (2007, background): “Hougaard system mentioned just above Joe’s BB5 family and the classes of copulas introduced by Galambos 1975, Husler and Reiss 1989, and Tawn 1988; 3. Meta-elliptical copulas described, e.g., in Fang et al. 2002 or Abdous et al. 2005, most notably the normal, the Student, and the Cauchy copulas; a”
The Grouped t-Copula with an Application to Credit Risk (2003, neutral): “The distribution of X is referred to as a meta-t distribution (see Fang, Fang, and Kotz 2002 ).”
Pair-Copula Constructions of Multivariate Copulas (2010, background): “Both the Gaussian and thet-copula are examples of elliptical copulas (see [ 18 , 20]).”
Bivariate drought frequency analysis using the copula method (2012, background): “However, only a few of them have found practical applications (Joe 1997; Nelsen 2006; Capéraà et al. 2000; Fang et al. 2002; Abdous et al. 2004).”