# Mixtures of Generalized Hyperbolic Distributions and Mixtures of Skew-t Distributions for Model-Based Clustering with Incomplete Data

## TL;DR

This paper introduces flexible mixture models based on generalized hyperbolic and skew-t distributions for robust clustering of incomplete, heavy-tailed, and asymmetric data, with an EM algorithm for parameter estimation and missing data imputation.

## Contribution

It develops an analytically feasible EM algorithm for mixture models with missing data, extending robust clustering methods to handle arbitrary missing patterns.

## Key findings

- The proposed methods outperform mean imputation in clustering accuracy.
- Simulation studies demonstrate robustness across various missing data proportions.
- Real data application confirms practical effectiveness.

## Abstract

Robust clustering from incomplete data is an important topic because, in many practical situations, real data sets are heavy-tailed, asymmetric, and/or have arbitrary patterns of missing observations. Flexible methods and algorithms for model-based clustering are presented via mixture of the generalized hyperbolic distributions and its limiting case, the mixture of multivariate skew-t distributions. An analytically feasible EM algorithm is formulated for parameter estimation and imputation of missing values for mixture models employing missing at random mechanisms. The proposed methodologies are investigated through a simulation study with varying proportions of synthetic missing values and illustrated using a real dataset. Comparisons are made with those obtained from the traditional mixture of generalized hyperbolic distribution counterparts by filling in the missing data using the mean imputation method.