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Finite Mixture of Skewed Distributions

  • Book
  • © 2018

Overview

Authors:
  1. Víctor Hugo Lachos Dávila

    1. Department of Statistics, University of Connecticut, Storrs Mansfield, USA

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  2. Celso Rômulo Barbosa Cabral

    1. Department of Statistics, Federal University of Amazonas, Manaus, Brazil

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  3. Camila Borelli Zeller

    1. Department of Statistics, Federal University of Juiz de Fora, Juiz de Fora, Brazil

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  • Uses a flexible class of probability distributions for modeling data with skewness behavior, discrepant observations and population heterogeneity instead nonparametric methods
  • Explores methods that are implemented in the R package mixsmsn
  • Enhances the spread of ideas that are currently trickling through the literature of mixture models

Part of the book series: SpringerBriefs in Statistics (BRIEFSSTATIST)

Part of the book sub series: SpringerBriefs in Statistics - ABE (BRIEFSABE)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. Motivation

    • Víctor Hugo Lachos Dávila, Celso Rômulo Barbosa Cabral, Camila Borelli Zeller
    Pages 1-5

  3. Maximum Likelihood Estimation in Normal Mixtures

    • Víctor Hugo Lachos Dávila, Celso Rômulo Barbosa Cabral, Camila Borelli Zeller
    Pages 7-13

  4. Scale Mixtures of Skew-Normal Distributions

    • Víctor Hugo Lachos Dávila, Celso Rômulo Barbosa Cabral, Camila Borelli Zeller
    Pages 15-36

  5. Univariate Mixture Modeling Using SMSN Distributions

    • Víctor Hugo Lachos Dávila, Celso Rômulo Barbosa Cabral, Camila Borelli Zeller
    Pages 37-56

  6. Multivariate Mixture Modeling Using SMSN Distributions

    • Víctor Hugo Lachos Dávila, Celso Rômulo Barbosa Cabral, Camila Borelli Zeller
    Pages 57-76

  7. Mixture Regression Modeling Based on SMSN Distributions

    • Víctor Hugo Lachos Dávila, Celso Rômulo Barbosa Cabral, Camila Borelli Zeller
    Pages 77-93

  8. Back Matter

    Pages 95-101
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Keywords

About this book

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.


Reviews

“The monograph is well written … and will be very useful to researchers using finite mixture models as it discusses contemporary methods used in such modelling.” (Ravi Sreenivasan, zbMATH 1428.62006, 2020)

Authors and Affiliations

  • Department of Statistics, University of Connecticut, Storrs Mansfield, USA

    Víctor Hugo Lachos Dávila

  • Department of Statistics, Federal University of Amazonas, Manaus, Brazil

    Celso Rômulo Barbosa Cabral

  • Department of Statistics, Federal University of Juiz de Fora, Juiz de Fora, Brazil

    Camila Borelli Zeller

About the authors

Victor Hugo Lachos Dávila 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 Rômulo 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 São 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.

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