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.

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.

Klappentext
Dirichlet and Related Distributions: Theory, Methods and Applications

Kai 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 Kong

Man-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

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.

Acknowledgments.

List of abbreviations.

List of symbols.

List of figures.

List of tables.

1 Introduction.

1.1 Motivating examples.

1.2 Stochastic representation and the ^d₌operator.

1.3 Beta and inverted beta distributions.

1.4 Some useful identities and integral formulae.

1.5 The Newton-Raphson algorithm.

1.6 Likeliho…