Finite mixture-of-gamma distributions: estimation, inference, and model-based clustering

• Published in: Advances in data analysis and classification Vol. 13; no. 4; pp. 1053 - 1082
• Main Authors: Young, Derek S., Chen, Xi, Hewage, Dilrukshi C., Nilo-Poyanco, Ricardo
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2019; Springer Nature B.V
• Subjects: Algorithms; Chemistry and Earth Sciences; Clustering; Computer Science; Computer simulation; Data Mining and Knowledge Discovery; Economic models; Economics; Finance; Habituation (learning); Health Sciences; Humanities; Inference; Insurance; Law; Management; Mathematics and Statistics; Maximum likelihood estimation; Medicine; Physics; Regular Article; Skewed distributions; Statistical Theory and Methods; Statistics; Statistics for Business; Statistics for Engineering; Statistics for Life Sciences; Statistics for Social Sciences; Starting values; Mixturegram; Identifiability; Finite mixture models; 62P15; ECM algorithms; 62H30; Multivariate Gaussian copula; 62F03
• ISSN: 1862-5347; 1862-5355
• DOI: 10.1007/s11634-019-00361-y

Finite mixtures of (multivariate) Gaussian distributions have broad utility, including their usage for model-based clustering. There is increasing recognition of mixtures of asymmetric distributions as powerful alternatives to traditional mixtures of Gaussian and mixtures of t distributions. The present work contributes to that assertion by addressing some facets of estimation and inference for mixtures-of-gamma distributions, including in the context of model-based clustering. Maximum likelihood estimation of mixtures of gammas is performed using an expectation–conditional–maximization (ECM) algorithm. The Wilson–Hilferty normal approximation is employed as part of an effective starting value strategy for the ECM algorithm, as well as provides insight into an effective model-based clustering strategy. Inference regarding the appropriateness of a common-shape mixture-of-gammas distribution is motivated by theory from research on infant habituation. We provide extensive simulation results that demonstrate the strong performance of our routines as well as analyze two real data examples: an infant habituation dataset and a whole genome duplication dataset.