Finite mixture modeling using shape mixtures of the skew scale mixtures of normal distributions

Abstract

This paper introduces the shape mixtures of the skew scale mixtures of normal distribution which are contained additional shape parameters to regulate skewness and kurtosis. We present a finite mixture model for this new family of distributions, which is a novel model-based tool for clustering heterogeneous data in the presence of skewed and heavy-tailed outcomes. The maximum likelihood estimates of the parameters of the proposed models are obtained by developing an Expectation Conditional Maximization Either algorithm. The numerical performance of the proposed methodology is illustrated through simulated and real data examples.