On fundamental skew distributions

By Reinaldo Boris Arellano-Valle, Marc G. Genton. 2005

374 citations recorded by the source corpus.

Subfields: Global and Planetary Change, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/825812a11c1fc659040831e674bfac4cf2e4aaa1

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In Global and Planetary Change

In Statistics and Probability

Citations in the corpus

A Constructive Representation of Univariate Skewed Distributions (2006, background): “In addition, recent research has shown that it is possible to extend models such as the one in (4) even to the case when G is not a distribution (Arellano-Valle and Genton, 2003).”
Shannon Entropy and Mutual Information for Multivariate Skew‐Elliptical Distributions (2013, background): “A flexible class of location-scale models is defined by the so-called skew-elliptical family of distributions; see Branco & Dey (2001), Azzalini & Capitanio (1999, 2003), Arellano-Valle & Azzalini (2006), Arellano-Valle & Genton (2005, 2010a, 2010b), and the book edited by Genton (2004).”
On matrix variate skew-normal distributions (2005, background): “Although the extension from the normal to skew-normal appears to be unique in the univariate case, there are many different ways to extend in the multivariate case, depending on what properties of the multivariate normal we would like the multivariate skew-normal distribution to preserve and what mo”
A New Class of Skew-Normal Distributions (2004, methodology): “The class of distributions we study in this article is closely related to the skew-normal (SN) distribution introduced by Azzalini (1985) and defined as follows: a random variable X has skew-normal distribution with asymmetry parameter l 2 R if f ðx jlÞ 1⁄4 2fðxÞFðlxÞ x 2 R; ð1:1Þ where fð Þ and Fð ”
On the exact distribution of the maximum of absolutely continuous dependent random variables (2008, background): “Then Arellano-Valle and Genton (2005) say that X has a k-dimensional fundamental skew (FUS) distribution with probability density function: f XðxÞ ¼ K 1m f YðxÞQmðxÞ; x 2 R k, (1) where QmðxÞ ¼ PðZX0jY ¼ xÞ and Km ¼ EðQmðYÞÞ ¼ PðZX0Þ.”
Bayesian Inference for Skew-normal Linear Mixed Models (2007, methodology): “Proof See Arellano-Valle et al. (2005).”
On Families of Distributions with Shape Parameters (2015, neutral): “Or perhaps, one wishes to use several-parameter univariate distributions as conditional distributions, either wholly, raising the difficulties of consistent conditional specification (Arnold et al., 1999), or in conjunction with one or more marginals using some of the basic rules of probability (e.g”
The Skew‐normal Distribution and Related Multivariate Families * (2005, background): “These formulations include proposals by Sahu et al. (2003), Liseo & Loperfido (2003a), González-Farı́as et al. (2004a, b) and Arellano-Valle & Genton (2005).”
Skew-normal Linear Mixed Models (2005, methodology): “It is, however, in the class of fundamental skew-normal distributions considered by Arellano-Valle and Genton (2005) (see also, (2.”
LIKELIHOOD BASED INFERENCE FOR SKEW-NORMAL INDEPENDENT LINEAR MIXED MODELS (2010, methodology): “1), this model corresponds to that introduced by Azzalini and Dalla-Valle (1996), with properties extensively studied in Azzalini and Capitanio (1999), and in Arellano-Valle and Genton (2005b). Let Z = Y−μ.”
A unified view on skewed distributions arising from selections (2006, methodology): “We start from the most general class of fundamental skewed distributions (Arellano-Valle & Genton 2005) and by successive specialization steps work down to the very specific skew-normal distribution of Azzalini (1985).”
On the Unification of Families of Skew‐normal Distributions (2006, methodology): “…(CSN) of González-Farı́as et al. (2004), the hierarchical skew-normal (HSN) of Liseo & Loperfido (2003), the fundamental skew-normal (FUSN) of Arellano-Valle & Genton (2005), the multivariate skew-normal of Gupta et al. (2004), the skew-normal of Sahu et al. (2003); although on a slightly…”