Statistical applications of the multivariate skew normal distribution

By Adelchi Azzalini, A. Capitanio. 2009

1,391 citations recorded by the source corpus.

Azzalini and Dalla Valle have recently discussed the multivariate skew normal distribution which extends the class of normal distributions by the addition of a shape parameter. The first part of the present paper examines further probabilistic properties of the distribution, with special emphasis on aspects of statistical relevance. Inferential and other statistical issues are discussed in the following part, with applications to some multivariate statistics problems, illustrated by numerical examples. Finally, a further extension is described which introduces a skewing factor of an elliptical density.

Subfields: Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/c8894f3ed8edf76954689ec70523d7592bcd0dd0

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In Management Science and Operations Research

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Citations in the corpus

Compositional Data Analysis: Where Are We and Where Should We Be Heading? (2005, neutral): “A welcome addition is the multivariate logistic skew normal (Mateu-Figueras, 2003; Mateu-Figueras, Barcel´ o-Vidal, and Pawlowsky-Glahn, 1998) based on the multivariate skew normal class introduced by Azzalini and Dalla Valle (1996) and further developed by Azzalini and Capitanio (1999) .”
LIKELIHOOD BASED INFERENCE FOR SKEW-NORMAL INDEPENDENT LINEAR MIXED MODELS (2010, background): “5), the conditional distribution of the bi given (Yi, Ui) = (yi, ui) belong to the extended skew-normal (EST) family of distributions (Azzalini and Capitanio (1999)), and its pdf is”
Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations (2009, positive): “, 1991; Weir and Pettitt, 2000), see also Banerjee et al. (2004) for many more examples. Models for spatial log-Gaussian Cox processes (Møller et al., 1998) are also in this class. Spatial models can also include 1D structures, like splines which model various covariate effects, see for example Nata”
Multivariate log‐skew‐elliptical distributions with applications to precipitation data (2009, methodology): “Dalla Valle (1996), Azzalini and Capitanio (1999) , Capitanio et al. (2003), and Azzalini (2005).”
Robust Likelihood Methods Based on the Skew‐t and Related Distributions (2008, methodology): “The first one, which will be implemented in this study for the ST distribution, is similar to the procedure proposed by Azzalini & Capitanio (1999).”
Skew scale mixtures of normal distributions: Properties and estimation (2011, neutral): “…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).”
GOODNESS-OF-FIT TESTS FOR THE SKEW-NORMAL DISTRIBUTION (2001, methodology): “outcomes that fall in the kth interval in n repetitions of the experiment; (3) The 2 test statistic with degree of freedoms K 1 is then defined as”
Analyzing skewed data by power normal model (2008, background): “Monti (2003) notes that the profile likelihood function for λ might be unbounded, so that the estimate is ˆ λ = ±∞, even when the data are generated by a model with finite λ. Other authors, such as Liseo (1990) and Azzalini and Capitanio (1999) , have investigated the behaviour of the estimates of ”
Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution (2003, methodology): “Other properties of quadratic forms of SN variables are given by Azzalini & Capitanio (1999) , Genton et al. (2001) and Loperfido (2001).”
A SKEW-SYMMETRIC REPRESENTATION OF MULTIVARIATE DISTRIBUTIONS (2002, positive): “Because of our Proposition 2, Proposition 6 is equivalent to Proposition 2 in Azzalini and Capitanio (2003). We give however an alternative proof, see the Appendix.”
Generalized skew-Cauchy distribution ☆ (2007, methodology): “The multivariate skew-normal distribution has also been considered by Azzalini and Dalla Valle (1996), Azzalini and Capitanio (1999), Gupta and Kollo (2003), and Gupta et al. (2004a).”
Generalized skew-elliptical distributions and their quadratic forms (2005, methodology): “Azzalini and Capitanio (1999) analyzed body fat and body mass indices of the athletes in the AIS data set, under the assumption that they came from a skewnormal distribution. They computed the quadratic forms of the data and used Healy's plot (Healy (1968)) to obtain a graphical display of fit.”
A heteroscedastic measurement error model based on skew and heavy-tailed distributions with known error variances (2018, background): “For additional properties related to the SN and the skew-t distributions, the interested reader is referred to [14,20], respectively.”
RELIABILITY STUDIES OF THE SKEW-NORMAL DISTRIBUTION AND ITS APPLICATION TO A STRENGTH-STRESS MODEL (2001, background): “1) has been recently studied by Azzalini and Dalla Valle [8] and Azzalini and Capitanio [9].”