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Lecture Notes in Statistics
cover

Finite Form Representations for Meijer G and Fox H Functions

Applied to Multivariate Likelihood Ratio Tests Using Mathematica®, MAXIMA and R

Authors: Coelho, Carlos A., Arnold, Barry C.

  • 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  
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eBook $84.99
price for USA (gross)
  • The eBook version of this title will be available soon
  • Due: February 7, 2020
  • ISBN 978-3-030-28790-0
  • Digitally watermarked, DRM-free
  • Included format:
  • ebooks can be used on all reading devices
Softcover $109.99
price for USA
  • Customers within the U.S. and Canada please contact Customer Service at +1-800-777-4643, Latin America please contact us at +1-212-460-1500 (24 hours a day, 7 days a week). Pre-ordered printed titles are excluded from promotions.
  • Due: January 10, 2020
  • ISBN 978-3-030-28789-4
  • Free shipping for individuals worldwide
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.

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.

Buy this book

eBook $84.99
price for USA (gross)
  • The eBook version of this title will be available soon
  • Due: February 7, 2020
  • ISBN 978-3-030-28790-0
  • Digitally watermarked, DRM-free
  • Included format:
  • ebooks can be used on all reading devices
Softcover $109.99
price for USA
  • Customers within the U.S. and Canada please contact Customer Service at +1-800-777-4643, Latin America please contact us at +1-212-460-1500 (24 hours a day, 7 days a week). Pre-ordered printed titles are excluded from promotions.
  • Due: January 10, 2020
  • ISBN 978-3-030-28789-4
  • Free shipping for individuals worldwide
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Bibliographic Information

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
Series Title
Lecture Notes in Statistics
Series Volume
223
Copyright
2019
Publisher
Springer International Publishing
Copyright Holder
Springer Nature Switzerland AG
eBook ISBN
978-3-030-28790-0
DOI
10.1007/978-3-030-28790-0
Softcover ISBN
978-3-030-28789-4
Series ISSN
0930-0325
Edition Number
1
Number of Pages
XVIII, 515
Number of Illustrations
41 b/w illustrations, 116 illustrations in colour
Topics