|  | Ng, Kai Wang / Tian, Guo-Liang / Tang, Man-Lai
Dirichlet and Related Distributions
Theory, Methods and Applications
Wiley Series in Probability and Statistics
 1. Auflage April 2011
87,90 Euro
2011. 336 Seiten, Hardcover
ISBN 978-0-470-68819-9 - John Wiley & Sons
Preis inkl. Mehrwertsteuer zzgl. Versandkosten.
|
Probekapitel
| Jetzt kaufen   
E-Books sind auch über alle bekannten E-Book Shops erhältlich.
|
| Kurzbeschreibung
In probability and statistics, the Dirichlet distribution often denoted Dir(03b1), is a family of continuous multivariate probability distributions parametrized by the vector 03b1 of positive reals. Providing a comprehensive review on inverted Dirichlet, Dirichlet-multinomial and generalized Dirichlet distributions (GDD), this book includes new results and developments in this area. The authors introduce two new families of distributions (GDD and NDD) and looks at new applications of generalized DD in sample surveys. The discussion of methodologies examines a wide range of applications, including medical science biological science and social science.
Aus dem Inhalt
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.
1.3 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 MDPs 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 MLEs of the Dirichlet parameters.
2.8 Generalized method of moments estimation.
2.9 Estimation based on linear models.
2.10 Application in estimating 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 nonignorable 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 the 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 hyper-Dirichlet distribution.
8.3 The scaled Dirichlet distribution.
8.4 The mixed Dirichlet distribution.
8.5 The Liouville distribution.
8.6 The generalized Liouville distribution.
Appendix A: Some useful S-plus Codes.
References.
Author Index.
Subject Index.
|
|
|
|
