Download or read book Finite Mixture Distributions written by B. Everitt and published by Springer Science & Business Media. This book was released on 2013-03-08 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite mixture distributions arise in a variety of applications ranging from the length distribution of fish to the content of DNA in the nuclei of liver cells. The literature surrounding them is large and goes back to the end of the last century when Karl Pearson published his well-known paper on estimating the five parameters in a mixture of two normal distributions. In this text we attempt to review this literature and in addition indicate the practical details of fitting such distributions to sample data. Our hope is that the monograph will be useful to statisticians interested in mixture distributions and to re search workers in other areas applying such distributions to their data. We would like to express our gratitude to Mrs Bertha Lakey for typing the manuscript. Institute oj Psychiatry B. S. Everitt University of London D. l Hand 1980 CHAPTER I General introduction 1. 1 Introduction This monograph is concerned with statistical distributions which can be expressed as superpositions of (usually simpler) component distributions. Such superpositions are termed mixture distributions or compound distributions. For example, the distribution of height in a population of children might be expressed as follows: h(height) = fg(height: age)f(age)d age (1. 1) where g(height: age) is the conditional distribution of height on age, and/(age) is the age distribution of the children in the population.
Download or read book On the Estimation of Parameters of a Finite Mixture of Distributions written by A. B. M. Lutful Kabir and published by . This book was released on 1966 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Finite Mixture Models written by Geoffrey McLachlan and published by John Wiley & Sons. This book was released on 2004-03-22 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: An up-to-date, comprehensive account of major issues in finitemixture modeling This volume provides an up-to-date account of the theory andapplications of modeling via finite mixture distributions. With anemphasis on the applications of mixture models in both mainstreamanalysis and other areas such as unsupervised pattern recognition,speech recognition, and medical imaging, the book describes theformulations of the finite mixture approach, details itsmethodology, discusses aspects of its implementation, andillustrates its application in many common statisticalcontexts. Major issues discussed in this book include identifiabilityproblems, actual fitting of finite mixtures through use of the EMalgorithm, properties of the maximum likelihood estimators soobtained, assessment of the number of components to be used in themixture, and the applicability of asymptotic theory in providing abasis for the solutions to some of these problems. The author alsoconsiders how the EM algorithm can be scaled to handle the fittingof mixture models to very large databases, as in data miningapplications. This comprehensive, practical guide: * Provides more than 800 references-40% published since 1995 * Includes an appendix listing available mixture software * Links statistical literature with machine learning and patternrecognition literature * Contains more than 100 helpful graphs, charts, and tables Finite Mixture Models is an important resource for both applied andtheoretical statisticians as well as for researchers in the manyareas in which finite mixture models can be used to analyze data.
Download or read book Statistical Analysis of Finite Mixture Distributions written by D. M. Titterington and published by . This book was released on 1985 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, the authors give a complete account of the applications, mathematical structure and statistical analysis of finite mixture distributions.
Download or read book Finite Mixture and Markov Switching Models written by Sylvia Frühwirth-Schnatter and published by Springer Science & Business Media. This book was released on 2006-11-24 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: The past decade has seen powerful new computational tools for modeling which combine a Bayesian approach with recent Monte simulation techniques based on Markov chains. This book is the first to offer a systematic presentation of the Bayesian perspective of finite mixture modelling. The book is designed to show finite mixture and Markov switching models are formulated, what structures they imply on the data, their potential uses, and how they are estimated. Presenting its concepts informally without sacrificing mathematical correctness, it will serve a wide readership including statisticians as well as biologists, economists, engineers, financial and market researchers.
Download or read book Parameter Estimation for a Finite Mixture Model in High Dimensional Applications written by Qinfang Xiang and published by . This book was released on 2006 with total page 106 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Finite mixture models have found use in the analysis of high dimensional data such as result from microarray experiments. A common goal of a microarray experiment is to identify genes that express differentially between two types of tissues or between two experimental conditions. Some investigators found that the distribution of P-values from tests for differential genetic expression contains useful information regarding several quantities of interest. A uniform-beta mixture distribution (mix-o-matic) has been employed to model this distribution...This dissertation covers three topics: 1) the performance of interval estimates of model parameters using three computational methods including a comparison of the computational methods; 2: a relatively recent approach based on a number theoretic method for obtaining MLEs, its extensions and a comparison to Newton-type methods; 3) FDR estimation in the mix-o-matic and a comparison with eight other techniques for estimating FDR, all techniques making use of information in the distribution of P-values"--Abstract, leaf iii.
Download or read book Finite Mixture Models written by Geoffrey McLachlan and published by Wiley-Interscience. This book was released on 2004-04-05 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: An up-to-date, comprehensive account of major issues in finite mixture modeling This volume provides an up-to-date account of the theory and applications of modeling via finite mixture distributions. With an emphasis on the applications of mixture models in both mainstream analysis and other areas such as unsupervised pattern recognition, speech recognition, and medical imaging, the book describes the formulations of the finite mixture approach, details its methodology, discusses aspects of its implementation, and illustrates its application in many common statistical contexts. Major issues discussed in this book include identifiability problems, actual fitting of finite mixtures through use of the EM algorithm, properties of the maximum likelihood estimators so obtained, assessment of the number of components to be used in the mixture, and the applicability of asymptotic theory in providing a basis for the solutions to some of these problems. The author also considers how the EM algorithm can be scaled to handle the fitting of mixture models to very large databases, as in data mining applications. This comprehensive, practical guide: * Provides more than 800 references-40% published since 1995 * Includes an appendix listing available mixture software * Links statistical literature with machine learning and pattern recognition literature * Contains more than 100 helpful graphs, charts, and tables Finite Mixture Models is an important resource for both applied and theoretical statisticians as well as for researchers in the many areas in which finite mixture models can be used to analyze data.
Download or read book Estimation of Parameters for Finite Mixtures of Pearson Type III Distributions written by Charalampos I. Saraidaridis and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On the Estimation of Parameters in Mixtures of Distributions written by Duane C. Boes and published by . This book was released on 1969 with total page 7 pages. Available in PDF, EPUB and Kindle. Book excerpt: The report is divided into the following sections: (1) list of publications, (2) minimax unbiased estimation of the mixed distribution for finite mixtures, (3) on the output of a queueing system, and (4) mixed regression. (Author).
Download or read book Estimation of Parameters of a Finite Mixture of Truncated Distributions written by A. B. M. Lutful Kabir and published by . This book was released on 1971 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Estimation of Parameters of a Finite Mixture of Truncated Distribution written by A. B. M. Lutful Kabir and published by . This book was released on 1971 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Mixture Models written by Weixin Yao and published by CRC Press. This book was released on 2024-04-18 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mixture models are a powerful tool for analyzing complex and heterogeneous datasets across many scientific fields, from finance to genomics. Mixture Models: Parametric, Semiparametric, and New Directions provides an up-to-date introduction to these models, their recent developments, and their implementation using R. It fills a gap in the literature by covering not only the basics of finite mixture models, but also recent developments such as semiparametric extensions, robust modeling, label switching, and high-dimensional modeling. Features Comprehensive overview of the methods and applications of mixture models Key topics include hypothesis testing, model selection, estimation methods, and Bayesian approaches Recent developments, such as semiparametric extensions, robust modeling, label switching, and high-dimensional modeling Examples and case studies from such fields as astronomy, biology, genomics, economics, finance, medicine, engineering, and sociology Integrated R code for many of the models, with code and data available in the R Package MixSemiRob Mixture Models: Parametric, Semiparametric, and New Directions is a valuable resource for researchers and postgraduate students from statistics, biostatistics, and other fields. It could be used as a textbook for a course on model-based clustering methods, and as a supplementary text for courses on data mining, semiparametric modeling, and high-dimensional data analysis.
Download or read book Essays on finite mixture models written by Abram van Dijk and published by Rozenberg Publishers. This book was released on 2009 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite mixture distributions are a weighted average of a finite number of distributions. The latter are usually called the mixture components. The weights are usually described by a multinomial distribution and are sometimes called mixing proportions. The mixture components may be the same type of distributions with di®erent parameter values but they may also be completely different distributions. Therefore, finite mixture distributions are very °exible for modeling data. They are frequently used as a building block within many modern econometric models. The specification of the mixture distribution depends on the modeling problem at hand. In this thesis, we introduce new applications of finite mixtures to deal with several di®erent modeling issues. Each chapter of the thesis focusses on a specific modeling issue. The parameters of some of the resulting models can be estimated using standard techniques but for some of the chapters we need to develop new estimation and inference methods. To illustrate how the methods can be applied, we analyze at least one empirical data set for each approach. These data sets cover a wide range of research fields, such as macroeconomics, marketing, and political science. We show the usefulness of the methods and, in some cases, the improvement over previous methods in the literature.
Download or read book Mixtures written by Kerrie L. Mengersen and published by John Wiley & Sons. This book was released on 2011-05-03 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book uses the EM (expectation maximization) algorithm to simultaneously estimate the missing data and unknown parameter(s) associated with a data set. The parameters describe the component distributions of the mixture; the distributions may be continuous or discrete. The editors provide a complete account of the applications, mathematical structure and statistical analysis of finite mixture distributions along with MCMC computational methods, together with a range of detailed discussions covering the applications of the methods and features chapters from the leading experts on the subject. The applications are drawn from scientific discipline, including biostatistics, computer science, ecology and finance. This area of statistics is important to a range of disciplines, and its methodology attracts interest from researchers in the fields in which it can be applied.
Download or read book Handbook of Mixture Analysis written by Sylvia Fruhwirth-Schnatter and published by CRC Press. This book was released on 2019-01-04 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mixture models have been around for over 150 years, and they are found in many branches of statistical modelling, as a versatile and multifaceted tool. They can be applied to a wide range of data: univariate or multivariate, continuous or categorical, cross-sectional, time series, networks, and much more. Mixture analysis is a very active research topic in statistics and machine learning, with new developments in methodology and applications taking place all the time. The Handbook of Mixture Analysis is a very timely publication, presenting a broad overview of the methods and applications of this important field of research. It covers a wide array of topics, including the EM algorithm, Bayesian mixture models, model-based clustering, high-dimensional data, hidden Markov models, and applications in finance, genomics, and astronomy. Features: Provides a comprehensive overview of the methods and applications of mixture modelling and analysis Divided into three parts: Foundations and Methods; Mixture Modelling and Extensions; and Selected Applications Contains many worked examples using real data, together with computational implementation, to illustrate the methods described Includes contributions from the leading researchers in the field The Handbook of Mixture Analysis is targeted at graduate students and young researchers new to the field. It will also be an important reference for anyone working in this field, whether they are developing new methodology, or applying the models to real scientific problems.
Download or read book Mixture Models and Applications written by Nizar Bouguila and published by Springer. This book was released on 2019-08-13 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on recent advances, approaches, theories and applications related to mixture models. In particular, it presents recent unsupervised and semi-supervised frameworks that consider mixture models as their main tool. The chapters considers mixture models involving several interesting and challenging problems such as parameters estimation, model selection, feature selection, etc. The goal of this book is to summarize the recent advances and modern approaches related to these problems. Each contributor presents novel research, a practical study, or novel applications based on mixture models, or a survey of the literature. Reports advances on classic problems in mixture modeling such as parameter estimation, model selection, and feature selection; Present theoretical and practical developments in mixture-based modeling and their importance in different applications; Discusses perspectives and challenging future works related to mixture modeling.
Download or read book Handbook of Market Research written by Christian Homburg and published by Springer. This book was released on 2021-12-03 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this handbook, internationally renowned scholars outline the current state-of-the-art of quantitative and qualitative market research. They discuss focal approaches to market research and guide students and practitioners in their real-life applications. Aspects covered include topics on data-related issues, methods, and applications. Data-related topics comprise chapters on experimental design, survey research methods, international market research, panel data fusion, and endogeneity. Method-oriented chapters look at a wide variety of data analysis methods relevant for market research, including chapters on regression, structural equation modeling (SEM), conjoint analysis, and text analysis. Application chapters focus on specific topics relevant for market research such as customer satisfaction, customer retention modeling, return on marketing, and return on price promotions. Each chapter is written by an expert in the field. The presentation of the material seeks to improve the intuitive and technical understanding of the methods covered.
