Generalized skew-elliptical distributions and their quadratic forms

By Marc G. Genton, Nicola Maria Rinaldo Loperfido. 2005

193 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/0b885dae9a27b60f61811eeda36ea88c5a146afe

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In Statistics and Probability

Citations in the corpus

Locally Efficient Semiparametric Estimators for Generalized Skew-Elliptical Distributions (2005, unknown): “Generalized skew-elliptical (GSE) distributions have been introduced by Genton and Loperfido (2005).”
Skew scale mixtures of normal distributions: Properties and estimation (2011, unknown): “…2003), skew-Cauchy distributions (Arnold and Beaver, 2000), skew-slash distributions (Wang and Genton, 2006), skew-slash-t distributions (Tan and Peng, 2006), skew-elliptical distributions (Azzalini and Capitanio, 1999; Branco and Dey, 2001; Sahu, Dey and Branco, 2003; Genton and Loperfido, 2005).”
A Constructive Representation of Univariate Skewed Distributions (2006, background): “Also, the focus of this paper is different from that of Genton and Loperfido (2005) who define the class of generalized skew-elliptical distributions, with density 2f(y)π(y), motivated by invariance of even functions, such as quadratic forms, to the skewing function π (given certain restrictions on ”
Skew-symmetric distributions and Fisher information -- a tale of two densities (2012, methodology): “, we obtain the class of skew-elliptical distributions as defined by Azzalini and Capitanio [6], itself a subclass of the generalized skew-elliptical distributions of Genton and Loperfido [15] where is left unspecified.”
Bayesian inference for shape mixtures of skewed distributions, with application to regression analysis (2008, background): “When f is the pdf of an elliptically contoured distribution, the family (1) defines generalized skew-elliptical distributions studied by Genton and Loperfido (2005).”
Skewed distributions in finance and actuarial science: a review (2015, methodology): “and Harrington (1988) document significant levels of skewness in insurance stock returns for a sample of property–liability companies for the time period 1970–1983 (see also Cummins and Nye 1980). Similar findings are reported for the life insurance sector (see, for example, Gentry and Pike 1970; Ha”
The multivariate skew-slash distribution (2006, methodology): “(2001) for the skew-normal distribution, Genton and Loperfido (2005) for generalized skew-elliptical distributions, and by Wang et al. (2004) for skew-symmetric distributions.”
Skew-normal Linear Mixed Models (2005, background): “In a more general way, we can replace in (2.2) the asymmetric part (or skewing function; see Genton and Loperfido, 2001) Φ1(·) by an arbitrary function Q(·) on [0, 1], which depends on y trough an even real function (or antisymmetric function; see Arellano-Valle and del Pino, 2003), say w(y), and…”
The Skew‐normal Distribution and Related Multivariate Families * (2005, background): “The above formulation is in the form presented by Azzalini & Capitanio (2003) and, in a slightly different way, by Genton & Loperfido (2005); despite the discrepancy in publication dates, these two papers have been developed independently and more or less simultaneously.”
A New Spatial Skew-Normal Random Field Model (2007, background): “Distributions in the class are also very similar to the generalized skew-elliptical distributions introduced recently by Genton and Loperfido ( 2005 ).”
Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution (2003, background): “A result that is similar to proposition 2 for the case when f is an elliptical distribution has been given by Genton and Loperfido (2002).”
On fundamental skew distributions (2005, background): “As was noted by Arellano-Valle et al.[2], if X is aC-random vector, thenKm = P(X > 0) = 2−m, so that (1.6) reduces to f (z|Qm) = 2mfk(z)Qm(z), z ∈ Rk. (1.8) If fk is a symmetric density onRk, thenQm can be interpreted as a skewing function, which in general does not satisfy the condition given by Ge”
Flexible Class of Skew‐Symmetric Distributions (2004, background): “Genton & Loperfido (2002) considered the subfamily of generalized skew-elliptical (GSE) distributions for which the pdf f in (1) is elliptically contoured rather than only symmetric.”