Finite Form Representations for Meijer G and Fox H Functions: Applied to Multivariate Likelihood Ratio Tests Using Mathematica®, MAXIMA and R

Carlos A. Coelho, Barry Arnold

Research output: Book/ReportBookpeer-review

Abstract

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.
Original languageEnglish
Place of PublicationCham, Switzerland
PublisherSpringer
Edition1st
ISBN (Electronic)978-3-030-28790-0
ISBN (Print)978-3-030-28789-4
DOIs
Publication statusPublished - 2019

Publication series

NameLecture Notes in Statistics
PublisherSpringer
Volume223
ISSN (Print)0930-0325

Keywords

  • Likelihood ratio tests
  • exact distributions
  • Meijer G function
  • Fox H function
  • GIG (Generalized Integer Gamma) distribution
  • EGIG distribution
  • Invariance
  • Mathematica
  • Maxima
  • R
  • Multivariate Analysis

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