A multivariate skew normal distribution

By Arjun K. Gupta, G. González-Farías, J. Domínguez-Molina. 2004

847 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/a2e74f07bf573c1922d817b59b60c32b1a0188ed

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Citations in the corpus

The Logarithmic Skew-Normal Distributions are Moment-Indeterminate (2009, background): “Then the conditional distribution of Z1, given Z2 > 0 (usually ignored and, thus, called a hidden truncation at the mean), is SN(λ(ρ)), where λ(ρ) = ρ/√1 − ρ2 (see, e.g. Azzalini and Dalla Valle (1996)).”
Locally Efficient Semiparametric Estimators for Generalized Skew-Elliptical Distributions (2005, neutral): “distribution, and we choose a parametric model π(x) = �( αT x) for the skewing function, where � is the univariate standard normal cumulative distribution function (cdf ), then (2) is the probability density function of the multivariate skew-normal distribution ( Azzalini and Dalla Valle 1996 ).”
Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution (2003, background): “The ‘general multivariate skew normal distribution’ mentioned by Gupta, Gonzales-Farias and Dominguez-Molina (2001, section 5) is even more general since they adopt a which is the the -dimensional normal distribution function.”
Skew-symmetric distributions and Fisher information -- a tale of two densities (2012, background): “Azzalini and Dalla Valle [8] and Azzalini and Capitanio [6] consider multivariate skew-normal distributions resulting from replacing in (1.”
Robust linear mixed models with skew-normal independent distributions from a Bayesian perspective (2009, neutral): “As a special case, this new class contains, the skew-normal distribution (Azzalini and Dalla-Valle, 1996), skew-t distribution (Azzalini and Capitanio, 2003; Gupta, 2003), skew-slash distribution (Wang and Genton, 2006), skew-contaminated normal distribution and all the symmetric family of NI…”
On the Unification of Families of Skew‐normal Distributions (2006, positive): “The multivariate SN class has been studied by Azzalini & Dalla Valle (1996) and Azzalini & Capitanio (1999), and subsequently by several authors, with intense developments in various directions, often considering nonnormal symmetric families as the starting point in place of the normal class.”
Output Assessment for Monte Carlo Simulations via the Score Statistic (2006, methodology): “We obtain 10,000 samples each, from three skew-normal distributions (Azzalina and Valle 1996) which are very similar to each other and to the target distribution SN(1.14, 1,−1), (5.1) OUTPUT ASSESSMENT FOR MONTE CARLO SIMULATIONS 195 SN(1.29, 1,−2), (5.2) and SN(1.6, 1.3,−5).”
Model-Based Clustering (2016, methodology): “One of these skew-normal formulations is given by Azzalini and Valle (1996) and examined further by Azzalini and Capitanio (1999) and others.”
Bayesian inference for shape mixtures of skewed distributions, with application to regression analysis (2008, background): “fZ(z) = 2f(z)FW0|Z0=z ( ηz √ 1 + τ2z2 ) , (11)”
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.”
Modelling interval data with Normal and Skew-Normal distributions (2012, background): “A more general model that overcomes these limitations may be obtained by considering the family of Skew-Normal distributions (see, for instance, [1–4]).”
The Skew‐normal Distribution and Related Multivariate Families * (2005, result): “Many of the above results have appeared in Azzalini & Dalla Valle (1996) and in Azzalini & Capitanio (1999), where the focus is on the case s ¼ 0.”
A New Fatigue Life Model Based on the Family of Skew-Elliptical Distributions (2006, background): “…distribution, whose principle results are accredited to Azzalini (1985), Azzalini and Capitanio (1999), Azzalini and Dalla Valle (1996), and Gupta et al. (2004), among others, great strides have been made in the skew-elliptical distribution theory as seen in works done by Branco and Dey…”