EMMIXcskew: An R Package for the Fitting of a Mixture of Canonical Fundamental Skew t-Distributions

Abstract

This paper presents the R package EMMIXcskew for the fitting of the canonical fundamental skew t-distribution (CFUST) and finite mixtures of CFUST distributions (FMCFUST) via maximum likelihood (ML). The CFUST distribution provides a flexible family to model non-normal data, with parameters for capturing skewness and heavy-tails in the data. It formally encompasses the normal, t, and skew normal distributions as special and/or limiting cases. A few other versions of the skew t-distributions are also nested within the CFUST distribution. In this paper, an expectation-maximization (EM) algorithm is described for computing the ML estimates of the parameters of the FM-CFUST model, and different strategies for initializing the algorithm are discussed and illustrated. The methodology is implemented in the EMMIXcskew package, and examples are presented using two real datasets. The EMMIXcskew package contains functions to fit the FM-CFUST model, including procedures for generating different initial values. Additional features include random sample generation and contour visualization in 2D and 3D.