A Multivariate Skew-Normal Mean-Variance Mixture Distribution and Its Application to Environmental Data with Outlying Observations

Abstract

The presence of outliers, skewness, kurtosis, and dependency are well-known challenges while fitting distributions to many data sets. Developing multivariate distributions that can properly accomodate all these aspects has been the aim of several researchers. In this regard, we introduce here a new multivariate skew-normal mean-variance mixture based on Birnbaum–Saunders distribution. The resulting model is a good alternative to some skewed distributions, especially the skew-t model. The proposed model is quite flexible in terms of tail behavior and skewness, and also displays good performance in the presence of outliers. For the determination of maximum likelihood estimates, a computationally efficient Expectation-Conditional-Maximization (ECM) algorithm is developed. The performance of the proposed estimation methodology is illustrated through Monte Carlo simulation studies as well as with some real life examples.

Keywords

• Multivariate distribution
• Birnbaum–Saunders
• ECM algorithm
• Outliers
• Mean-variance mixtures