Paper of the Month: October 2019

Once a month during the academic year, the statistics faculty select a paper for our students to read and discuss. Papers are selected based on their impact or historical value, or because they contain useful techniques or results.

A. Azzalini and A. Dalla-Valle (1996). The Multivariate Skew Normal Distribution, Biometrika, Volume 83, Number 4, 715-726.

Notes preparer: Victor Hugo Lachos

In this paper Azzalini and Dalla Valle introduced the multivariate skew normal (MSN) distribution which extends the class of multivariate normal distributions by the addition of a shape parameter to regulate skewness. Several properties are discussed with emphasis on the bivariate case. In a subsequent paper, published in the JRSS B [Azzalini and Capitanio (1999). Statistical applications of the multivariate skew normal distribution. Volume 61, Number 3, 715-726], further probabilistic properties of the distribution are examined, with special emphasis on aspects of statistical relevance.

Since the introduction of the MSN, several multivariate distributions have been proposed, such as, the multivariate skew-t distribution or the class of skew-elliptical distributions. Our faculty Dipak Dey published an interesting paper in JMVA [Branco and Dey (2001). A general class of multivariate skew-elliptical distributions. Volume 79, Number 1, 99-113]. Most importantly, is that distributions generated starting from the MSN distributions has been widely used in many applications such as mixed-effects models, finite mixture models, spatial models, measurement error models, just to mention a few. Personally, I wrote my PhD thesis using this distribution in 2004, and recently I have written a book entitled “Finite Mixtures of Skewed Distributions” published by Springer, which is based on the multivariate skew-elliptical distributions and the R package mixsmsn.