Dirichlet and Related Distributions: Theory, Methods and Applications 1st Edition by Kai Wang Ng (PDF)

Description

The Dirichlet distribution appears in many areas of application, which include modelling of compositional data, Bayesian analysis, statistical genetics, and nonparametric inference. This book provides a comprehensive review of the Dirichlet distribution and two extended versions, the Grouped Dirichlet Distribution (GDD) and the Nested Dirichlet Distribution (NDD), arising from likelihood and Bayesian analysis of incomplete categorical data and survey data with non-response. The theoretical properties and applications are also reviewed in detail for other related distributions, such as the inverted Dirichlet distribution, Dirichlet-multinomial distribution, the truncated Dirichlet distribution, the generalized Dirichlet distribution, Hyper-Dirichlet distribution, scaled Dirichlet distribution, mixed Dirichlet distribution, Liouville distribution, and the generalized Liouville distribution.Key Features: Presents many of the results and applications that are scattered throughout the literature in one single volume. Looks at the most recent results such as survival function and characteristic function for the uniform distributions over the hyper-plane and simplex; distribution for linear function of Dirichlet components; estimation via the expectation-maximization gradient algorithm and application; etc. Likelihood and Bayesian analyses of incomplete categorical data by using GDD, NDD, and the generalized Dirichlet distribution are illustrated in detail through the EM algorithm and data augmentation structure. Presents a systematic exposition of the Dirichlet-multinomial distribution for multinomial data with extra variation which cannot be handled by the multinomial distribution. S-plus/R codes are featured along with practical examples illustrating the methods. Practitioners and researchers working in areas such as medical science, biological science and social science will benefit from this book.

User’s Reviews

Editorial Reviews: Review “The book is a treasure chest both for researchers in (mathematical and applied) statistics and for practitioners. Researchers will especially pro_t from the impressive survey of the literature and the many references, while practitioners will acknowledge the many real data examples and the S-PLUS code provided in the appendix.” (Zentralblatt MATH, 1 December 2012) From the Inside Flap Dirichlet and Related Distributions: Theory, Methods and ApplicationsKai Wang Ng, Professor and Head, and Guo-Liang Tian, Associate Professor, Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong KongMan-Lai Tang, Associate Professor, Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong. London School of Economics and Political Science, UK The Dirichlet distribution appears in many areas of application, which include modelling of compositional data, Bayesian analysis, statistical genetics, and nonparametric inference. This book provides a comprehensive review of the Dirichlet distribution and two extended versions, the Grouped Dirichlet Distribution (GDD) and the Nested Dirichlet Distribution (NDD), arising from likelihood and Bayesian analysis of incomplete categorical data and survey data with non-response.The theoretical properties and applications are also reviewed in detail for other related distributions, such as the inverted Dirichlet distribution, Dirichlet-multinomial distribution, the truncated Dirichlet distribution, the generalized Dirichlet distribution, Hyper-Dirichlet distribution, scaled Dirichlet distribution, mixed Dirichlet distribution, Liouville distribution, and the generalized Liouville distribution.Key Features: Presents many of the results and applications that are scattered throughout the literature in one single volume. Looks at the most recent results such as survival function and characteristic function for the uniform distributions over the hyper-plane and simplex; distribution for linear function of Dirichlet components; estimation via the expectation-maximization gradient algorithm and application; etc. Likelihood and Bayesian analyses of incomplete categorical data by using GDD, NDD, and the generalized Dirichlet distribution are illustrated in detail through the EM algorithm and data augmentation structure. Presents a systematic exposition of the Dirichlet-multinomial distribution for multinomial data with extra variation which cannot be handled by the multinomial distribution. S-plus/R codes are featured along with practical examples illustrating the methods. Practitioners and researchers working in areas such as medical science, biological science and social science will benefit from this book.www.wiley.com/go/dirichlet From the Back Cover Dirichlet and Related Distributions: Theory, Methods and ApplicationsKai Wang Ng, Professor and Head, and Guo-Liang Tian, Associate Professor, Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong KongMan-Lai Tang, Associate Professor, Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong. London School of Economics and Political Science, UK The Dirichlet distribution appears in many areas of application, which include modelling of compositional data, Bayesian analysis, statistical genetics, and nonparametric inference. This book provides a comprehensive review of the Dirichlet distribution and two extended versions, the Grouped Dirichlet Distribution (GDD) and the Nested Dirichlet Distribution (NDD), arising from likelihood and Bayesian analysis of incomplete categorical data and survey data with non-response.The theoretical properties and applications are also reviewed in detail for other related distributions, such as the inverted Dirichlet distribution, Dirichlet-multinomial distribution, the truncated Dirichlet distribution, the generalized Dirichlet distribution, Hyper-Dirichlet distribution, scaled Dirichlet distribution, mixed Dirichlet distribution, Liouville distribution, and the generalized Liouville distribution.Key Features: Presents many of the results and applications that are scattered throughout the literature in one single volume. Looks at the most recent results such as survival function and characteristic function for the uniform distributions over the hyper-plane and simplex; distribution for linear function of Dirichlet components; estimation via the expectation-maximization gradient algorithm and application; etc. Likelihood and Bayesian analyses of incomplete categorical data by using GDD, NDD, and the generalized Dirichlet distribution are illustrated in detail through the EM algorithm and data augmentation structure. Presents a systematic exposition of the Dirichlet-multinomial distribution for multinomial data with extra variation which cannot be handled by the multinomial distribution. S-plus/R codes are featured along with practical examples illustrating the methods. Practitioners and researchers working in areas such as medical science, biological science and social science will benefit from this book.www.wiley.com/go/dirichlet About the Author Kai Wang Ng, Department of Statistics and Actuarial Science, The University of Hong Kong. Ng has published over seventy journal articles and book chapters and co-authored five books. Guo-Liang Tian, Department of Statistics and Actuarial Science, The University, of Hong Kong. His research areas include generalized mixed-effects models for longitudinal data, hierarchical modeling, and applied Bayesian methods in biostatistical models. Man-Lai Tang, Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐

⭐

⭐

⭐

⭐

⭐

⭐

⭐

⭐

Keywords

Free Download Dirichlet and Related Distributions: Theory, Methods and Applications 1st Edition in PDF format
Dirichlet and Related Distributions: Theory, Methods and Applications 1st Edition PDF Free Download
Download Dirichlet and Related Distributions: Theory, Methods and Applications 1st Edition 2011 PDF Free
Dirichlet and Related Distributions: Theory, Methods and Applications 1st Edition 2011 PDF Free Download
Download Dirichlet and Related Distributions: Theory, Methods and Applications 1st Edition PDF
Free Download Ebook Dirichlet and Related Distributions: Theory, Methods and Applications 1st Edition