The Skew‐normal Distribution and Related Multivariate Families *

By Adelchi Azzalini. 2005

768 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/9973abb4e77d640ab6f0c40e8077d190b1185f57

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In Statistics and Probability

Citations in the corpus

Sine-skewed circular distributions (2011, background): “Perhaps the best known example of this approach is the one leading to the skew-normal distribution of Azzalini (1985, 2005) .”
Partially Collapsed Gibbs Samplers: Illustrations and Applications (2009, background): “,Z(s−1)1,β1,β2, ,Yobs), is an extended skew-normal distribution (Azzalini 2005) because p(Zs1,Zs2|Z11, .”
Robust Likelihood Methods Based on the Skew‐t and Related Distributions (2008, methodology): “For the SN family, a more regular behaviour of the log-likelihood function can be achieved by a suitable re-parameterization, which has also the advantage of simpler interpretation of the parameters; for a discussion of this point, see, for instance Section 2.4 of Azzalini (2005).”
Maximum penalized likelihood estimation for skew-normal and skew-t distributions (2012, background): “For a general overview of the subject, we refer the readers to the book edited by Genton (2004) and the review paper of Azzalini (2005); a concise account on the skew-normal distribution, including its multivariate version, is given by Azzalini (2011).”
Skewed distributions in finance and actuarial science: a review (2015, methodology): “Mardia’s skewness and kurtosis for the MSN distribution were originally presented in Azzalini and Capitanio (1999). When X ∼ MESNn(η, , −1ψ, τ), it is straightforward to show that 1 = ξ3(τ ) 2(ψ −1ψ)3 [1 + ψ −1ψ{1 + ξ2(τ )}]3 , 2 = ξ4(τ )(ψ T −1ψ)2 [1 + ψ −1ψ{1 + ξ2(τ )}]2 .”
Multivariate log‐skew‐elliptical distributions with applications to precipitation data (2009, methodology): “For more details and applications of the multivariate skew-normal distribution, see Azzalini and Dalla Valle (1996), Azzalini and Capitanio Copyright © 2009 John Wiley & Sons, Ltd. Environmetrics 2010; 21: 318–340 DOI: 10.1002/env (1999), Capitanio et al. (2003), and Azzalini (2005).”
A Heckman Selection-t Model (2012, methodology): “A bivariate skew-normal distribution (Azzalini and Dalla Valle 1996; Azzalini and Capitanio 1999; Azzalini 2005) and a bivariate skew-t distribution (Azzalini and Capitanio 2003) are two appealing candidates.”
Construction of multivariate distributions: a review of some recent results (2008, background): “Two recent reviews of these classes appear in the book edited by Genton (2004) and the paper by Azzalini (2005).”
Bayesian inference for shape mixtures of skewed distributions, with application to regression analysis (2008, background): “book edited by Genton (2004), in Azzalini (2005) , in Arellano-Valle and Azzalini (2006), and”
A New Spatial Skew-Normal Random Field Model (2007, background): “Azzalini ( 2005 ) provides a review of recent developments in this area.”