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Dirichlet and Related Distributions: Theory, Methods and Applications Book

Dirichlet and Related Distributions: Theory, Methods and Applications
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Dirichlet and Related Distributions: Theory, Methods and Applications, This book provides a comprehensive review on the Dirichlet distribution including its basic properties, marginal and conditional distributions, cumulative distribution and survival functions. The authors provide insight into new materials such as survi, Dirichlet and Related Distributions: Theory, Methods and Applications
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  • Dirichlet and Related Distributions: Theory, Methods and Applications
  • Written by author Kai Wang Ng
  • Published by Wiley, John & Sons, Incorporated, 6/15/2011
  • This book provides a comprehensive review on the Dirichlet distribution including its basic properties, marginal and conditional distributions, cumulative distribution and survival functions. The authors provide insight into new materials such as survi
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Authors

Preface.

Acknowledgments.

List of Figures.

List of Tables.

List of Abbreviations.

List of Symbols.

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 Likelihood in Missing Data Problems.

1.7 Bayesian Missing Data Problems (MDP) and Inversion of Bayes' Formula.

1.8 Basic Statistical Distributions.

2 Dirichlet Distribution.

2.1 Definition and Basic Properties.

2.2 Marginal and Conditional Distributions.

2.3 Survival Function and Cumulative Distribution Function.

2.4 Characteristic Functions.

2.5 Distribution for Linear Function of Dirichlet Random Vector.

2.6 Characterizations.

2.7 Maximum Likelihood Estimates (MLEs) of the Dirichlet Parameters.

2.8 Generalized Method of Moments Estimation.

2.9 Estimation Based on Linear Models.

2.10 Application in Estimating Receiver Operating Characteristic (ROC) Area.

3 Grouped Dirichlet Distribution.

3.1 Three Motivating Examples.

3.2 Density Function.

3.3 Basic Properties.

3.4 Marginal Distributions.

3.5 Conditional Distributions.

3.6 Extension to Multiple Partitions.

3.7 Statistical Inferences: Likelihood Function with GDD Form.

3.8 Statistical Inferences: Likelihood Function beyond GDD Form.

3.9 Applications under Non-ignorable Missing Data Mechanism.

4 Nested Dirichlet Distribution.

4.1 Density function.

4.2 Two Motivating Examples.

4.3 Stochastic Representation, Mixed Moments and Mode.

4.4 Marginal Distributions.

4.5 Conditional Distributions.

4.6 Connection with Exact Null Distribution for Sphericity Test.

4.7 Large-Sample Likelihood Inference.

4.8 Small-Sample Bayesian Inference.

4.9 Applications.

4.10 A Brief Historical Review.

5 Inverted Dirichlet Distribution.

5.1 Definition through Density Function.

5.2 Definition through Stochastic Representation.

5.3 Marginal and Conditional Distributions.

5.4 Cumulative Distribution Function and Survival Function.

5.5 Characteristic Function.

5.6 Distribution for Linear Function of Inverted Dirichlet Vector.

5.7 Connection with Other Multivariate Distributions.

5.8 Applications.

6 Dirichlet-Multinomial Distribution.

6.1 Probability Mass Function.

6.2 Moments of the Distribution.

6.3 Marginal and Conditional Distributions.

6.4 Conditional Sampling Method.

6.5 The Method of Moments Estimation.

6.6 The Method of Maximum Likelihood Estimation.

6.7 Applications.

6.8 Testing the Multinomial Assumption against the Dirichlet-Multinomial Alternative.

7 Truncated Dirichlet Distribution.

7.1 Density function.

7.2 Motivating Examples.

7.3 Conditional Sampling Method.

7.4 Gibbs Sampling Method.

7.5 The Constrained Maximum Likelihood Estimates.

7.6 Application to Misclassification.

7.7 Application to Uniform Design of Experiment with Mixtures.

8 Other Related Distributions.

8.1 The Generalized Dirichlet Distribution.

8.2 The Hyperdirichlet Distribution.

8.3 The Scaled Dirichlet Distribution.

8.4 The Mixed Dirichlet Distribution.

8.5 The Liouville Distribution.

8.6 The Generalized Liouville Distribution.

A Some Useful S-plus Codes.

A.1 Multinomial Distribution.

A.2 Dirichlet Distribution.

A.3 Grouped Dirichlet Distribution.

A.4 Nested Dirichlet Distribution.

A.5 Dirichlet-Multinomial Distribution.

References.

Author Index.

Subject Index.


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Dirichlet and Related Distributions: Theory, Methods and Applications, This book provides a comprehensive review on the Dirichlet distribution including its basic properties, marginal and conditional distributions, cumulative distribution and survival functions.
The authors provide insight into new materials such as survi, Dirichlet and Related Distributions: Theory, Methods and Applications

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Dirichlet and Related Distributions: Theory, Methods and Applications, This book provides a comprehensive review on the Dirichlet distribution including its basic properties, marginal and conditional distributions, cumulative distribution and survival functions.
The authors provide insight into new materials such as survi, Dirichlet and Related Distributions: Theory, Methods and Applications

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Dirichlet and Related Distributions: Theory, Methods and Applications, This book provides a comprehensive review on the Dirichlet distribution including its basic properties, marginal and conditional distributions, cumulative distribution and survival functions.
The authors provide insight into new materials such as survi, Dirichlet and Related Distributions: Theory, Methods and Applications

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