An EM algorithm for estimating the parameters of the skew generalized t -normal distribution with application to robust finite mixture modeling

AbstractThe present article describes an EM-type algorithm for estimation of the skew generalized t-normal (SGTN) distribution. The family of SGTN distributions can provide certain types of flexibility such as heavy tails and high kurtosis. The complexity of the SGTN distribution is traced to the ratio of the t density and distribution function of a normal distribution in the likelihood equations. To cope with this problem, we develop a feasible ECME algorithm for computing maximum likelihood estimates of model parameters via a selection mechanism. The proposed approach provides a robust parameter estimation method for the finite mixture model. Standard errors for the parameter estimates can be obtained via a general information-based method. Experimental results on simulated data and one real data example demonstrate the efficacy and usefulness of the proposed methodology.Keywords: ECME algorithmFinite mixture modelGeneralized t-normal distributionTruncated normal distribution AcknowledgmentsThe authors are grateful to the Co-Editors, the Associate Editor, and the anonymous referees for their valuable comments and constructive suggestions which had improved the content of this article greatly.Disclosure statementNo potential conflict of interest was reported by the authors.Additional informationFundingA.F. Desmond acknowledges the support of NSERC Canada under Discovery Grant no. 04537.