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Dedicated to one of the most outstanding researchers in the field
of statistics, this volume in honor of C.R. Rao, on the occasion of
his 100th birthday, provides a bird's-eye view of a broad spectrum
of research topics, paralleling C.R. Rao's wide-ranging research
interests. The book's contributors comprise a representative sample
of the countless number of researchers whose careers have been
influenced by C.R. Rao, through his work or his personal aid and
advice. As such, written by experts from more than 15 countries,
the book's original and review contributions address topics
including statistical inference, distribution theory, estimation
theory, multivariate analysis, hypothesis testing, statistical
modeling, design and sampling, shape and circular analysis, and
applications. The book will appeal to statistics researchers,
theoretical and applied alike, and PhD students. Happy Birthday,
C.R. Rao!
Dedicated to one of the most outstanding researchers in the field
of statistics, this volume in honor of C.R. Rao, on the occasion of
his 100th birthday, provides a bird's-eye view of a broad spectrum
of research topics, paralleling C.R. Rao's wide-ranging research
interests. The book's contributors comprise a representative sample
of the countless number of researchers whose careers have been
influenced by C.R. Rao, through his work or his personal aid and
advice. As such, written by experts from more than 15 countries,
the book's original and review contributions address topics
including statistical inference, distribution theory, estimation
theory, multivariate analysis, hypothesis testing, statistical
modeling, design and sampling, shape and circular analysis, and
applications. The book will appeal to statistics researchers,
theoretical and applied alike, and PhD students. Happy Birthday,
C.R. Rao!
This book depicts a wide range of situations in which there exist
finite form representations for the Meijer G and the Fox H
functions. Accordingly, it will be of interest to researchers and
graduate students who, when implementing likelihood ratio tests in
multivariate analysis, would like to know if there exists an
explicit manageable finite form for the distribution of the test
statistics. In these cases, both the exact quantiles and the exact
p-values of the likelihood ratio tests can be computed quickly and
efficiently. The test statistics in question range from common
ones, such as those used to test e.g. the equality of means or the
independence of blocks of variables in real or complex normally
distributed random vectors; to far more elaborate tests on the
structure of covariance matrices and equality of mean vectors. The
book also provides computational modules in Mathematica (R), MAXIMA
and R, which allow readers to easily implement, plot and compute
the distributions of any of these statistics, or any other
statistics that fit into the general paradigm described here.
Products of ratios of independent Gamma random variables (r.v.'s)
are relevant in many tests of hypotheses. Obtaining explicit
manageable expressions for their p.d.f. and c.d.f. is a challenging
problem. In this monograph we take this challenge. The book tries
to illustrate the use of several techniques, exhibiting a balanced
blend between theory and a good number of examples. A large number
of graphs and tables illustrate several particular aspects of the
distributions being studied. Besides the exact distribution, we
also consider near-exact ones, obtained through a new concept of
approximation of the characteristic function. Computational modules
are provided to implement all distributions developed. The approach
followed enabled an easy extension to the non-central case and to
negative power parameters, greatly widening the domain of
application of the results obtained. As particular immediate cases
we have the distribution of products and ratios of many known
distributions, among which folded T, folded Cauchy, Beta prime or
Beta second kind and, of course, F r.v.'s. The book is intended for
an audience at the graduate or post-graduate level, with focus on
Distribution Theory.
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