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Author Lachos Dávila, Víctor Hugo,
Title Finite Mixture of Skewed Distributions / Victor Hugo Lachos Davila, Celso Romulo Barbosa Cabral, Camila Borelli Zeller.
Imprint Cham, Switzerland : Springer, [2018]

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Author Lachos Dávila, Víctor Hugo,
Series Springer briefs in statistics. ABE.
SpringerBriefs in statistics. ABE.
Subject Mixture distributions (Probability theory)
Mathematical statistics -- Data processing.
Alt Name Cabral, Celso Rômulo Barbosa,
Zeller, Camila Borelli,
Description 1 online resource : illustrations.
Bibliography Note Includes bibliographical references and index.
Contents Intro; Preface; Contents; 1 Motivation; 2 Maximum Likelihood Estimation in Normal Mixtures; 2.1 EM Algorithm for Finite Mixtures; 2.2 Standard Errors; 3 Scale Mixtures of Skew-Normal Distributions; 3.1 Introduction; 3.2 SMN Distributions; 3.2.1 Examples of SMN Distributions; 3.3 Multivariate SMSN Distributions and Main Results; 3.3.1 Examples of SMSN Distributions; 3.3.2 A Simulation Study; 3.4 Maximum Likelihood Estimation; 3.5 The Observed Information Matrix; 4 Univariate Mixture Modeling Using SMSN Distributions; 4.1 Introduction; 4.2 The Proposed Model.
4.2.1 Maximum Likelihood Estimation via EM Algorithm4.2.2 Notes on Implementation; 4.3 The Observed Information Matrix; 4.3.1 The Skew-t Distribution; 4.3.2 The Skew-Slash Distribution; 4.3.3 The Skew-Contaminated Normal Distribution; 4.4 Simulation Studies; 4.4.1 Study 1: Clustering; 4.4.2 Study 2: Asymptotic Properties; 4.4.3 Study 3: Model Selection; 4.5 Application with Real Data; 5 Multivariate Mixture Modeling Using SMSN Distributions; 5.1 Introduction; 5.2 The Proposed Model; 5.2.1 Maximum Likelihood Estimation via EM Algorithm; 5.3 The Observed Information Matrix.
5.3.1 The Skew-Normal Distribution5.3.2 The Skew-t Distribution; 5.3.3 The Skew-Slash Distribution; 5.3.4 The Skew-Contaminated Normal Distribution; 5.4 Applications with Simulated and Real Data; 5.4.1 Consistency; 5.4.2 Standard Deviation; Number of Mixture Components; 5.4.3 Model Fit and Clustering; 5.4.4 The Pima Indians Diabetes Data; 5.5 Identifiability and Unboundedness; 6 Mixture Regression Modeling Based on SMSN Distributions; 6.1 Introduction; 6.2 The Proposed Model; 6.2.1 Maximum Likelihood Estimation via EM Algorithm; 6.2.2 Notes on Implementation; 6.3 Simulation Experiments.
6.3.1 Experiment 1: Parameter Recovery6.3.2 Experiment 2: Classification; 6.3.3 Experiment 3: Classification; 6.4 Real Dataset; References; Index.
Summary 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.-- Provided by publisher.
Note Vendor-supplied metadata.
Online resource; title from PDF title page (EBSCO, viewed November 15, 2018).
ISBN 9783319980294 (electronic bk.)
3319980297 (electronic bk.)
OCLC # 1065522905

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