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Product and Ratio of Generalized Gamma-Ratio Random Variables (Paperback)
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Product and Ratio of Generalized Gamma-Ratio Random Variables (Paperback)
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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.
General
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