‎em-type algorithm‎

This paper introduces an innovative family of statistical models called the multivariate skew scale-shape mixtures of normal distributions. These models serve as a versatile tool in statistical analysis by efficiently characterizing the skewed and leptokurtic nature commonly observed in multivariate datasets. Their applicability shines in real-world scenarios where data often deviate from standard statistical assumptions due to the presence of outliers. We present an EM-type algorithm designed for maximizing likelihood estimation and evaluate the model's effectiveness through real-world data applications. Through rigorous testing against various datasets, we assess the performance and practicality of the proposed algorithm in real statistical scenarios. The results demonstrate the remarkable performance of this new family of distributions.

‎The purpose of this paper is to extend the mixture factor analyzers (MFA) model \CG{to handle} missing and heavy-\CG{tailed} data‎. ‎In this model‎, ‎the distribution of factors loading and errors arise from the multivariate normal mean-variance mixture of‎ \CG{the} Birnbaum-Saunders (NMVBS) distribution‎. ‎By using the structures covariance matrix‎, ‎we introduce parsimonious MFA based on NMVBS distribution‎. ‎An Expectation Maximization (EM)-type algorithm is developed for parameter estimation‎. ‎Simulations study and real data sets represent the efficiency and performance of the proposed model‎.

In spite of widespread use as well as theoretical properties of the multivariate scale mixture normal distributions, practical studies show a lack of stability and robustness against asymmetric features such as asymmetry and heavy tails. In this paper, we develop a new multivariate model by assuming the Birnbaum-Saunders distribution for the mixing variable in the scale mix- tures restricted skew-normal distribution. An analytically simple and efficient EM-type algorithm is adopted for iteratively computing maximum likelihood estimate of model parameters. To account standard errors, the observed in- formation matrix is derived analytically by offering an information-based ap-proach. Results obtained from real and simulated datasets are reported toillustrate the practical utility of the proposed methodology.