Dirichlet and Related Distributions —— Theory, Methods and Applications

----- Dirichlet及相关分布：理论，方法及应用

ISBN: 9780470688199 出版年：2011 页码：338 Kai Wang Ng Guo-Liang Tian Wiley

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.