Physical description 
1 online resource : illustrations. 
Series 
Springer briefs in statistics. ABE 

SpringerBriefs in statistics. ABE.


Springer Mathematics and Statistics eBooks 2018 English+International

Bibliography 
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 SkewNormal 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 Skewt Distribution; 4.3.2 The SkewSlash Distribution; 4.3.3 The SkewContaminated 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 SkewNormal Distribution5.3.2 The Skewt Distribution; 5.3.3 The SkewSlash Distribution; 5.3.4 The SkewContaminated 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 skewnormal and skewed versions of some other classical symmetric distributions: the skewt (ST), the skewslash (SSL) and the skewcontaminated 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 EMtype 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 graduatelevel 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. 
Other author 
Cabral, Celso Rômulo Barbosa, author.


Zeller, Camila Borelli, author.


SpringerLink issuing body.

Subject 
Mixture distributions (Probability theory)


Mathematical statistics  Data processing.


Electronic books. 
ISBN 
9783319980294 (electronic bk.) 

3319980297 (electronic bk.) 

9783319980287 

3319980289 
