Finite Form Representations for Meijer G and Fox H Functions (häftad)
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Format
Häftad (Paperback / softback)
Språk
Engelska
Antal sidor
515
Utgivningsdatum
2019-12-14
Upplaga
1st ed. 2019
Förlag
Springer Nature Switzerland AG
Medarbetare
Arnold, Barry C.
Illustratör/Fotograf
129 farbige Tabellen 41 schwarz-weiße und 116 farbige Abbildungen Bibliographie
Illustrationer
116 Illustrations, color; 41 Illustrations, black and white; XVIII, 515 p. 157 illus., 116 illus. in
Dimensioner
234 x 156 x 27 mm
Vikt
745 g
Antal komponenter
1
Komponenter
1 Paperback / softback
ISBN
9783030287894

Finite Form Representations for Meijer G and Fox H Functions

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

av Carlos A Coelho, Barry C Arnold
Häftad,  Engelska, 2019-12-14
1505
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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.
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Carlos A Coelho, Barry C Arnold

Övrig information

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.

Innehållsförteckning

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.

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