I believe the paper is highly cited because it opens new possibilities of research from both theoretical and applied statistical aspects.

“This paper unifies these two ideas and proposes a very general class of probability distributions, which is useful from a solid theoretical foundation as well as for several other areas of applications.”

For years the multivariate normal distribution has been the main focus, or perhaps the only distribution used to model continuous data in statistics. Since in many situations it is not very realistic, most authors have been working under a more flexible class of probability distributions which includes the normal distribution that preserves some desirable properties.

In one direction, the departure from normality is incorporated through the elliptically contoured distribution, which preserves the symmetry, and in another direction the skew normal and related skewed distributions incorporates other features such as the shape of the distribution.

This paper unifies these two ideas and proposes a very general class of probability distributions, which is useful from a solid theoretical foundation as well as for several other areas of applications. On the one hand there remain several open questions, primarily among these being a search to find new properties, natural extensions, and how to make inference using the skew-elliptical models.

Statistics is a discipline of science that can be useful in many different fields of application. To use a more realistic distribution to model a data set is important in order to make an accurate inference. The skew normal class of distributions is a flexible and elegant class that is useful as a means to extend many statistical models, for example, adding asymmetry and kurtosis in the model.

I started working on elliptical distributions during my Ph.D. studies at the University of São Paulo (Brazil) with my supervisors Professor Pilar Iglesias and Professor Heleno Bolfarine. The idea to unify it with asymmetric models was given to me by Professor Dipak K. Dey during my post-doctoral research at the University of Connecticut (USA).

The first version of the paper, submitted to Journal of Multivariate Analysis, was written in a three-month period. Perhaps if we had worked longer on that, there could have emerged a more complete paper exploring special cases as, for example, the skew-t distribution. Now various authors have followed our work and concentrated on showing the importance of this distribution from several different aspects.

Well, after 2001, we could see some papers using skew-elliptical models within several different fields, including astronomy, finance, psychometrics, education, and spatial data. In consideration of this, I think that this theoretical paper could also be useful in making good statistical applications. And perhaps it could one day even be used to define social and political models.

In 2004, Professor Marc Genton edited a volume by Chapman and Hall on this subject entitled Skew-Elliptical Distributions and Their Applications: A Journey Beyond Normality, where we can examine some of the extensions and applications as mentioned here before.