A Multivariate Skew-Normal Mean-Variance Mixture Distribution and Its Application to Environmental Data with Outlying Observations
Mostafa Tamandi, N. Balakrishnan, Ahad Jamalizadeh, Mehdi Amiri · Journal of Statistical Theory and Applications · 2019
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.