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 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 inverted
Dirichlet distribution, Dirichlet-multinomial distribution, the
truncated Dirichlet distribution, the generalized Dirichlet
distribution, Hyper-Dirichlet distribution, scaled Dirichlet
distribution, mixed Dirichlet distribution, Liouville distribution,
and the generalized Liouville distribution.
Key Features: Presents many of the results and applications that
are scattered throughout the literature in one single volume.
Looks at the most recent results such as survival function and
characteristic function for the uniform distributions over the
hyper-plane and simplex; distribution for linear function of
Dirichlet components; estimation via the expectation-maximization
gradient algorithm and application; etc.
Likelihood and Bayesian analyses of incomplete categorical data by
using GDD, NDD, and the generalized Dirichlet distribution are
illustrated in detail through the EM algorithm and data
augmentation structure.Presents a systematic exposition of the
Dirichlet-multinomial distribution for multinomial data with extra
variation which cannot be handled by the multinomial
distribution.
S-plus/R codes are featured along with practical examples
illustrating the methods.
Practitioners and researchers working in areas such as medical
science, biological science and social science will benefit from
this book.
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