This book presents recent results in finite mixtures of skewed distributions to prepare readers to undertake mixture models using scale mixtures of skew normal distributions (SMSN). For this purpose, the authors consider maximum likelihood estimation for univariate and multivariate finite mixtures where components are members of the flexible class of SMSN distributions. This subclass includes the entire family of normal independent distributions, also known as scale mixtures of normal distributions (SMN), as well as the skew-normal and skewed versions of some other classical symmetric distributions: the skew-t (ST), the skew-slash (SSL) and the skew-contaminated normal (SCN), for example. These distributions have heavier tails than the typical normal one, and thus they seem to be a reasonable choice for robust inference. The proposed EM-type algorithm and methods are implemented in the R package mixsmsn, highlighting the applicability of the techniques presented in the book.
This work is a useful reference guide for researchers analyzing heterogeneous data, as well as a textbook for a graduate-level course in mixture models. The tools presented in the book make complex techniques accessible to applied researchers without the advanced mathematical background and will have broad applications in fields like medicine, biology, engineering, economic, geology and chemistry.
Victor Hugo Lachos Davila is Professor in the Department of Statistics at the University of Connecticut, USA. His research interests are in the areas of asymmetric-elliptical distributions, mixed effects models, stochastic volatility models, finite mixture of distributions, spatial statistics and augmented models. In 2008, he won the Inter-American Statistical Institute Award for Excellence and, in 2012, he was distinguished with the "Zeferino Vaz Award" from the University of Campinas, Brazil. He has authored over 100 papers in several peer-reviewed journals.
Celso Romulo Barbosa Cabral is a Professor at the Federal University of Amazonas, Brazil, where he graduated in Statistics (1987). He received his Master's degree from the National Association of Pure and Applied Mathematics, IMPA, Brazil (1991) and his PhD (2000) in Statistics from the University of Sao Paulo, Brazil. His research focuses mainly on asymmetric distributions, measurement error models and finite mixtures of distributions.
Camila Borelli Zeller is a Professor at the Federal University of Juiz de Fora, Brazil. She holds a Master's degree (2006) and a PhD (2009) in Statistics, from the University of Campinas, Brazil. The main focus of her research is asymmetric distributions, linear models and finite mixtures of distributions.