LEADER 05501nam 2200697 450 001 9910130868703321 005 20230725053034.0 010 $a1-283-40560-1 010 $a9786613405609 010 $a1-119-99841-7 010 $a1-119-99586-8 010 $a1-119-99578-7 035 $a(CKB)3460000000003354 035 $a(EBL)699360 035 $a(OCoLC)794326221 035 $a(SSID)ssj0000507336 035 $a(PQKBManifestationID)11344051 035 $a(PQKBTitleCode)TC0000507336 035 $a(PQKBWorkID)10546443 035 $a(PQKB)11769543 035 $a(MiAaPQ)EBC699360 035 $a(EXLCZ)993460000000003354 100 $a20160513h20112011 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aDirichlet and related distributions $etheory, methods and applications /$fKai Wang Ng, Guo-Liang Tian, Man-Lai Tang 210 1$aChichester, England :$cWiley,$d2011. 210 4$dİ2011 215 $a1 online resource (338 p.) 225 1 $aWiley Series in Probability and Statistics 300 $aDescription based upon print version of record. 311 $a0-470-68819-X 320 $aIncludes bibliographical references and indexes. 327 $aDirichlet 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 327 $a1.5 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 327 $a1.8.2 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 327 $a2.5.1 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 327 $a2.7.1 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 327 $a2.10.4 Analyzing the mammogram data of breast cancer 330 $aThe Dirichlet distribution appears in many areas of application, which include modelling of compositional data, Bayesian analysis, statistical genetics, and nonparametric inference. This book provides a comprehensive review of the Dirichlet distribution and two extended versions, the Grouped Dirichlet Distribution (GDD) and the Nested Dirichlet Distribution (NDD), arising from likelihood and Bayesian analysis of incomplete categorical data and survey data with non-response. The theoretical properties and applications are also reviewed in detail for other related distributions, such as the in 410 0$aWiley series in probability and statistics. 606 $aDistribution (Probability theory) 606 $aDirichlet problem 615 0$aDistribution (Probability theory) 615 0$aDirichlet problem. 676 $a515.782 676 $a519.2/4 686 $aMAT029000$2bisacsh 700 $aNg$b Kai Wang$0102773 702 $aTian$b Guo-Liang 702 $aTang$b Man-Lai 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910130868703321 996 $aDirichlet and related distributions$92239880 997 $aUNINA