EM algorithm for mixture of skew-normal distributions fitted to grouped data

Abstract

Grouped data are frequently used in several fields of study. In this work, we use the expectation-maximization (EM) algorithm for fitting the skew-normal (SN) mixture model to the grouped data. Implementing the EM algorithm requires computing the one-dimensional integrals for each group or class. Our simulation study and real data analyses reveal that the EM algorithm not only always converges but also can be implemented in just a few seconds even when the number of components is large, contrary to the Bayesian paradigm that is computationally expensive. The accuracy of the EM algorithm and superiority of the SN mixture model over the traditional normal mixture model in modelling grouped data are demonstrated through the simulation and three real data illustrations. For implementing the EM algorithm, we use the package called ForestFit developed for R environment available at https://cran.r-project.org/web/packages/ForestFit/index.html.

Keywords:

• EM algorithm
• grouped data
• maximum likelihood method
• mixture distributions
• skew-normal distribution

Acknowledgments

The author would like to thank the Editor-in-Chief, an associate editor, and three referees for their valuable comments, which substantially improved the quality of the paper.

Disclosure statement

No potential conflict of interest was reported by the author.