A General Class of Multivariate Skew-Elliptical Distributions

By Máaarcia D. Branco, Dipak K. Dey. 2001

741 citations recorded by the source corpus.

This paper proposes a general class of multivariate skew-elliptical distributions. We extend earlier results on the so-called multivariate skew-normal distribution. This family of distributions contains the multivariate normal, Student's t, exponential power, and Pearson type II, but with an extra parameter to regulate skewness. We also obtain the moment generating functions and study some distributional properties. Several examples are provided.

Subfields: Safety, Risk, Reliability and Quality, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/304d23d39850b8df877b080deccf99206be217a3

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In Safety, Risk, Reliability and Quality

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Citations in the corpus

Characterization of the skew-normal distribution (2004, background): “The works of Azzalini and Dalla Valle (1996), Azzalini and Capitanio (2003), Arnold et al. (1993), Arnold and Beaver (2002), Gupta et al. (2002a) and Branco and Dey (2001) focused on the theoretical developments of various extensions and multivariate generalizations of the model.”
Robust linear mixed models with skew-normal independent distributions from a Bayesian perspective (2009, neutral): “Recently, Branco and Dey (2001) developed a new class of robust distributions, called scale mixtures of skew-normal (SMSN) distributions.”
Flexible Class of Skew‐Symmetric Distributions (2004, background): “…& Dey, 2001; Azzalini & Capitanio, 2003; Jones & Faddy, 2003; Sahu et al., 2003), skew-Cauchy (Arnold & Beaver, 2000) and other skewelliptical ones (Azzalini & Capitanio, 1999; Branco & Dey, 2001; Sahu et al., 2003) can be represented by the SS distribution (1) with appropriate choices of f and p.”
Multivariate log‐skew‐elliptical distributions with applications to precipitation data (2009, background): “ Branco and Dey (2001) present a special subclass of the skew-elliptical distributions, the”
Bayesian Inference for Skew-normal Linear Mixed Models (2007, background): “Studies on Multivariate skew-normal distributions are considered in Azzalini & DallaValle (1996), Branco & Dey (2001), among others.”
Skew-symmetric distributions and Fisher information -- a tale of two densities (2012, background): “The class of skew-elliptical distributions is also studied in detail by Branco and Dey [10], based, however, on a slightly different definition.”
A New Class of Skew-Normal Distributions (2004, background): “and Dalla Valle (4), Branco and Dey ( 5 ) and Arellano-Valle and Genton (6).”
Skew-normal Linear Mixed Models (2005, background): “Studies on multivariate skew-normal distributions are considered in Azzalini and Dalla Valle (1996), Azzalini and Capitanio (1999), Branco and Dey (2001), Sahu et al. (2003), among others.”
Robust Likelihood Methods Based on the Skew‐t and Related Distributions (2008, background): “The specific form which we will consider is the one studied by Branco & Dey (2001, 2002) and in equivalent forms by Azzalini & Capitanio (2003) and Gupta (2003); see also Kim & Mallick (2003) for additional results.”
On Families of Distributions with Shape Parameters (2015, positive): “Indeed, many publications on that topic (e.g. Branco & Dey, 2001, Arnold & Beaver, 2002, Azzalini & Capitanio, 2003, Arellano-Valle & Genton, 2005, Arellano-Valle, Branco & Genton, 2006, Kim, 2008) work in the multivariate case because it adds little more than notational complexity.”