Parameter estimation of the multivariate unrestricted skew-normal distribution using ECM algorithm

Abstract

The probability density function of the multivariate unrestricted skew-normal (SUN) distribution, corresponding to a screened normal density, allow to modeling skewness and kurtosis in data in terms of a skewness parameter vector and a truncation parameter matrix. These parameters are related to the shape and heavy-tails of the density. In this article, we present the Expectation/Conditional Maximization (ECM) algorithm for the SUN distribution based on a hierarchical stochastic representation. In addition, behavior of ECM algorithm’s steps is measured using an information theoretic approach based on Jeffrey’s divergence and related homogeneity test. Usefulness of the proposed method is illustrated by an application to Chilean economic perception data.

Keywords:

• ECM algorithm
• Genz’s method
• Jeffrey’s divergence
• Skew-normal
• Skewness
• Unified skew-normal

Acknowledgment

The authors thank the editor and two anonymous referees for their helpful comments and suggestions.

Disclosure statement

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this article.

Data availability statement

Data used in Sec. 4 are publicly available from the github repository at https://github.com/percepcioneseconomicas/indices/find/main. All R codes and datasets used in this article are available upon request from the corresponding author.

Notes

1 A methodological note about the building of this index is available at https://ceen.udd.cl/estudios-y-publicaciones/ice/.

2 A methodological note about the building of this index is available at https://ceen.udd.cl/estudios-y-publicaciones/ipeco/.

Additional information

Funding

Research was fully supported by FONDECYT (Chile) grant No. 11190116.