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Lecture Notes in Statistics

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.

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  • 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 71,68 €
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  • ISBN 978-3-030-28790-0
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
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  • Immediate eBook download after purchase
Softcover 88,39 €
price for Spain (gross)
  • ISBN 978-3-030-28789-4
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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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.

Table of contents (7 chapters)

Table of contents (7 chapters)
  • Setting the Scene

    Pages 1-4

    Coelho, Carlos A. (et al.)

  • The Meijer G and Fox H Functions

    Pages 5-18

    Coelho, Carlos A. (et al.)

  • Multiple Products of Independent Beta Random Variables with Finite Form Representations for Their Distributions

    Pages 19-27

    Coelho, Carlos A. (et al.)

  • Finite Form Representations for Extended Instances of Meijer G and Fox H Functions

    Pages 29-70

    Coelho, Carlos A. (et al.)

  • Application of the Finite Form Representations of Meijer G and Fox H Functions to the Distribution of Several Likelihood Ratio Test Statistics

    Pages 71-452

    Coelho, Carlos A. (et al.)

Buy this book

eBook 71,68 €
price for Spain (gross)
  • ISBN 978-3-030-28790-0
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover 88,39 €
price for Spain (gross)
  • ISBN 978-3-030-28789-4
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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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

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