Finite Form Representations for Meijer G and Fox H Functions
Applied to Multivariate Likelihood Ratio Tests Using Mathematica®, MAXIMA and R
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Beschreibung
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®, 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.
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®, 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.Identifies situations in which there exist finite form representations of the Meijer G or the Fox H functions Enables readers to quickly and efficiently compute the exact quantiles and exact p-values of a number of likelihood ratio tests used in multivariate analysis Includes computational modules in R, Mathematica® and MAXIMA
Autor*in
Carlos A. Coelho
Themen in »Finite Form Representations for Meijer G and Fox H Functions«
tests on mean values and covariance structures likelihood ratio test statistics products of Beta distributed random variables finite representations of distributions for l.r.t. statistics Meijer G function Fox H function special functions Mathematica MAXIMA R exact distribution exact quantile exact p-value multivariate likelihood ratio tests multivariate analysis