The Dirichlet distribution appears in many areas of application,which include modelling of compositional data, Bayesian analysis,statistical genetics, and nonparametric inference. This bookprovides a comprehensive review of the Dirichlet distribution andtwo extended versions, the Grouped Dirichlet Distribution (GDD) andthe Nested Dirichlet Distribution (NDD), arising from likelihoodand Bayesian analysis of incomplete categorical data and surveydata with non-response.
The theoretical properties and applications are also reviewed indetail for other related distributions, such as the invertedDirichlet distribution, Dirichlet-multinomial distribution, thetruncated Dirichlet distribution, the generalized Dirichletdistribution, Hyper-Dirichlet distribution, scaled Dirichletdistribution, mixed Dirichlet distribution, Liouville distribution,and the generalized Liouville distribution.
Key Features:
* Presents many of the results and applications that arescattered throughout the literature in one single volume.
* Looks at the most recent results such as survival function andcharacteristic function for the uniform distributions over thehyper-plane and simplex; distribution for linear function ofDirichlet components; estimation via the expectation-maximizationgradient algorithm and application; etc.
* Likelihood and Bayesian analyses of incomplete categoricaldata by using GDD, NDD, and the generalized Dirichlet distributionare illustrated in detail through the EM algorithm and dataaugmentation structure.
* Presents a systematic exposition of the Dirichlet-multinomialdistribution for multinomial data with extra variation which cannotbe handled by the multinomial distribution.
* S-plus/R codes are featured along with practical examplesillustrating the methods.
Practitioners and researchers working in areas such as medicalscience, biological science and social science will benefit fromthis book.