Authors:
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
Part of the book series: Lecture Notes in Statistics (LNS, volume 223)
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Table of contents (7 chapters)
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Front Matter
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Back Matter
About this book
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.Keywords
- 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
Authors and Affiliations
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Department of Mathematics, Universidade NOVA de Lisboa, Caparica, Portugal
Carlos A. Coelho
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Department of Statistics, University of California, Riverside, USA
Barry C. Arnold
About the authors
Carlos A. Coelho is a Full Professor at the Mathematics Department of Nova University of Lisbon, Portugal. He obtained his Ph.D. in Biostatistics from the University of Michigan, USA. An Elected Member of the International Statistical Institute, he is primarily pursuing research in the fields of mathematical statistics and distribution theory, e.g. exact and near-exact distributions for likelihood ratio statistics used in multivariate analysis.
Barry C. Arnold is a Distinguished Professor in the Department of Statistics at the University of California, Riverside, USA. He holds a Ph.D. in Statistics from Stanford University. He is a Fellow of both the American Statistical Association and the Institute of Mathematical Statistics and a former Elected Member of the International Statistical Institute. His research interests include multivariate models, inequality measurement and ordered data.
Bibliographic Information
Book Title: Finite Form Representations for Meijer G and Fox H Functions
Book Subtitle: Applied to Multivariate Likelihood Ratio Tests Using Mathematica®, MAXIMA and R
Authors: Carlos A. Coelho, Barry C. Arnold
Series Title: Lecture Notes in Statistics
DOI: https://doi.org/10.1007/978-3-030-28790-0
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2019
Softcover ISBN: 978-3-030-28789-4Published: 14 December 2019
eBook ISBN: 978-3-030-28790-0Published: 13 December 2019
Series ISSN: 0930-0325
Series E-ISSN: 2197-7186
Edition Number: 1
Number of Pages: XVIII, 515
Number of Illustrations: 41 b/w illustrations, 116 illustrations in colour
Topics: Statistical Theory and Methods, Statistics and Computing/Statistics Programs, Applied Statistics