Finite Form Representations for Meijer G and Fox H Functions

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.

• Preface.- Setting the Scene.- The Meijer G and Fox H Functions.- Multiple Products of Independent Beta Random Variables with Finite Form Representations for Their Distributions.- Finite Form Representations for Extended Instances of Meijer G and Fox H Functions.- Application of the Finite Form Representations of Meijer G and Fox H Functions to the Distribution of Several Likelihood Ratio Test Statistics.- Mathematica, MAXIMA and R Packages to Implement the Likelihood Ratio Tests and Compute the Distributions in the Previous Chapter.- Approximate Finite Forms for the Cases not Covered by the Finite Representation Approach.- Index.