Finite mixture of skewed distributions
type: Item
instance of: scholarly article
title: Finite mixture of skewed distributions
zbMATH Open document ID: 1428.62006
DOI: 10.1007/978-3-319-98029-4
author: Celso Rômulo Barbosa Cabral
author: Camila Borelli Zeller
author: V. H. Lachos
published in: SpringerBriefs in Statistics
publication date: 2018-12-12T00:00:00Z
review text: This monograph published in Springer Briefs in Statistics is on finite mixture models and it presents results on finite scale mixtures of skew-normal distributions abbreviated as SMSN distributions. This class is a subclass of the skew-elliptical class and contains the entire family of independent normal distributions known as scale mixtures of normal distributions, in addition to the skew-normal, the skew-\(t\) and the skew-slash distributions. These distributions have tails heavier than the normal and are suitable for robust inference accommodating skewness, outliers and multimodality. Out of the six chapters, the first chapter gives a couple of motivating examples. The second chapter reviews the general theory of maximum likelihood estimation in finite mixture models with multivariate normal components, using the Expectation-Maximization (EM) algorithm with an explanation on the method of obtaining the standard error estimates for the EM estimators. The third chapter is on the SMSN distributions and contains examples of scale mixtures of normal distributions, discusses the multivariate SMSN distributions and their properties like moments, kurtosis, linear transformations, marginal and conditional distributions with examples, a simulation study and maximum likelihood estimation. Chapter 4 is on the univariate mixture modelling using SMSN distributions which is a flexible class, convenient for modelling data with skewness and population heterogeneity. An EM-type algorithm is developed for maximum likelihood estimation and the observed information matrix is obtained. The procedures are discussed with emphasis on finite mixtures of skew normal, skew-\(t\), skew slash and skew contaminated normal distributions. The algorithm is implemented in the R package mixsmsn. Under simulation studies, the ability of the model in clustering observations is investigated, some asymptotic properties of the estimates obtained using the proposed EM-type algorithm are investigated, mod…
Mathematics Subject Classification ID: 62-02
Mathematics Subject Classification ID: 62H30
Mathematics Subject Classification ID: 62E10
Mathematics Subject Classification ID: 60E05
Mathematics Subject Classification ID: 62F35
Mathematics Subject Classification ID: 62E15
Mathematics Subject Classification ID: 62E20
Mathematics Subject Classification ID: 62J05
zbMATH DE Number: 6992858
zbMATH Keywords: finite mixture models
zbMATH Keywords: skew normal
zbMATH Keywords: scale mixtures
zbMATH Keywords: EM algorithm
zbMATH Keywords: maximum likelihood estimation
zbMATH Keywords: R package
zbMATH Keywords: model selection
zbMATH Keywords: information matrix
zbMATH Keywords: clustering
reviewed by: Sreenivasan Ravi
describes a project that uses: mixsmsn
describes a project that uses: bayesmix
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-319-98029-4
OpenAlex ID: W2901279757
description: scientific article; zbMATH DE number 6992858