Mixtures of Power Exponential Distributions and Topics in Regression-based Mixture Models

Abstract

Mixture models continue to be the dominant framework for modelling heterogeneity in data. A family of mixtures of multivariate exponential power distributions that can robustly model varying tail-weight and peakedness of data is presented. A novel family of mixtures of symmetric Kotz-type distributions is also presented. In addition to modelling varying tail-weight and peakedness, this family can also account for anti-modal density shapes. Applications in model-based clustering are presented. Three types of regression-based mixture models, namely finite mixtures of regressions, finite mixtures of regression with concomitant variables, and cluster-weighted models are also extended for modelling multivariate correlated response variables in an unsupervised learning context. These models perform well on data with functional dependencies. Moreover, a family of parsimonious cluster-weighted models is presented that allows for modelling of generalized linear (binomial, Poisson, etc.) responses. Lastly, an extension of cluster-weighted models for dealing with censored competing risks data is presented via a mixture of accelerated failure time models.