Scale mixtures of multivariate centered skew-normal distributions

• Published in: Statistics and computing Vol. 34; no. 6
• Main Authors: de Freitas, João Victor B., Bondon, Pascal, Azevedo, Caio L. N., Reisen, Valdério A., Nobre, Juvêncio S.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01-12-2024; Springer Nature B.V
• Subjects: Artificial Intelligence; Bayesian analysis; Computer Science; Data recovery; Mixtures; Monte Carlo simulation; Multivariate analysis; Normal distribution; Original Paper; Probability and Statistics in Computer Science; Skewed distributions; Statistical inference; Statistical Theory and Methods; Statistics and Computing/Statistics Programs; Scale mixtures; Multivariate data; Centered skew-normal; Bayesian inference; Skewed data; Heavy-tailed data
• ISSN: 0960-3174; 1573-1375
• DOI: 10.1007/s11222-024-10512-7

The most popular approach for modeling multivariate data in many research areas is based on the multivariate normal distribution. However, this approach may not be suitable when dealing with data presenting skewness and/or heavy tail distribution. Thus, the scale mixtures of multivariate skew-normal distributions become an alternative distribution to deal with this scenario. In this context, we introduce the scale mixtures of multivariate centered skew-normal (MCSN) distributions to circumvent some inferential and interpretation problems. Some related properties of this family and Bayesian inference are presented. A Monte Carlo simulation study is carried out to evaluate the parameter recovery. The methodology is illustrated by analyzing a real data set where the new distributions outperform the MCSN distribution.