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