A generalized multivariate logistic model and EM algorithm based on the normal variance mean mixture representation
Jason A. Palmer, Kenneth Kreutz-Delgado, Scott Makeig · 2016
We present an EM algorithm for Maximum Likelihood estimation of the location, scale, and skew, and shape parameters of the z distribution, also known as the generalized logistic function (type IV). We use the Barndorff-Nielsen, Kent, and Sørensen representation of the z distribution as a Gaussian location-scale mixture to derive an EM algorithm for estimating the location, scale, skew, and shape parameters. We use a variational bound on the likelihood function to determine a monotonically converging closed form update for the skew (or drift) parameter. The algorithm also extends naturally to multivariate GLSM estimation using the Kolmogorov-Smirnov mixing density in odd dimensions.