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Dirichlet and Related Distributions : Theory, Methods and Applications.
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 Dirichl...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Chicester :
Wiley,
2011.
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| Colección: | Wiley series in probability and statistics.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Dirichlet and Related Distributions: Theory, Methods and Applications; Contents; Preface; 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; 1.2.1 Definition of stochastic representation; 1.2.2 More properties on the d = operator; 1.3 Beta and inverted beta distributions; 1.4 Some useful identities and integral formulae; 1.4.1 Partial-fraction expansion; 1.4.2 Cambanis-Keener-Simons integral formulae; 1.4.3 Hermite-Genocchi integral formula.
- 1.5 The Newton-Raphson algorithm1.6 Likelihood in missing-data problems; 1.6.1 Missing-data mechanism; 1.6.2 The expectation-maximization (EM) algorithm; 1.6.3 The expectation/conditional maximization (ECM) algorithm; 1.6.4 The EM gradient algorithm; 1.7 Bayesian MDPs and inversion of Bayes' formula; 1.7.1 The data augmentation (DA) algorithm; 1.7.2 True nature of Bayesian MDP: inversion of Bayes' formula; 1.7.3 Explicit solution to the DA integral equation; 1.7.4 Sampling issues in Bayesian MDPs; 1.8 Basic statistical distributions; 1.8.1 Discrete distributions.
- 1.8.2 Continuous distributions2 Dirichlet distribution; 2.1 Definition and basic properties; 2.1.1 Density function and moments; 2.1.2 Stochastic representations and mode; 2.2 Marginal and conditional distributions; 2.3 Survival function and cumulative distribution function; 2.3.1 Survival function; 2.3.2 Cumulative distribution function; 2.4 Characteristic functions; 2.4.1 The characteristic function of u ~ U(Tn); 2.4.2 The characteristic function of v ~ U(Tn); 2.4.3 The characteristic function of a Dirichlet random vector; 2.5 Distribution for linear function of a Dirichlet random vector.
- 2.5.1 Density for linear function of v ~ U(Vn)2.5.2 Density for linear function of u ~ U(Tn); 2.5.3 A unified approach to linear functions of variables and order statistics; 2.5.4 Cumulative distribution function for linear function of a Dirichlet random vector; 2.6 Characterizations; 2.6.1 Mosimann's characterization; 2.6.2 Darroch and Ratcliff's characterization; 2.6.3 Characterization through neutrality; 2.6.4 Characterization through complete neutrality; 2.6.5 Characterization through global and local parameter independence; 2.7 MLEs of the Dirichlet parameters.
- 2.7.1 MLE via the Newton-Raphson algorithm2.7.2 MLE via the EM gradient algorithm; 2.7.3 Analyzing serum-protein data of Pekin ducklings; 2.8 Generalized method of moments estimation; 2.8.1 Method of moments estimation; 2.8.2 Generalized method of moments estimation; 2.9 Estimation based on linear models; 2.9.1 Preliminaries; 2.9.2 Estimation based on individual linear models; 2.9.3 Estimation based on the overall linear model; 2.10 Application in estimating ROC area; 2.10.1 The ROC curve; 2.10.2 The ROC area; 2.10.3 Computing the posterior density of the ROC area.