Finite Form Representations for Meijer G and Fox H Functions: Applied to Multivariate Likelihood Ratio Tests Using Mathematica®, MAXIMA and R (Lecture Notes in Statistics, 223) - Softcover

Coelho, Carlos A.; Arnold, Barry C.

Softcover

ISBN 10: 3030287890 ISBN 13: 9783030287894

Publisher: Springer, 2019

Synopsis

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 this title

About the Author

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.

From the Back Cover

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.

Edition details

• Publisher: Springer
• Publication date: 2019
• Language: English
• ISBN 10: 3030287890
• ISBN 13: 9783030287894
• Binding: Paperback
• Edition number: 1
• Number of pages: 533