LEADER 03768nam 22005895 450 001 9910364956003321 005 20250505003907.0 010 $a3-030-28790-4 024 7 $a10.1007/978-3-030-28790-0 035 $a(CKB)4100000010013750 035 $a(MiAaPQ)EBC5996856 035 $a(DE-He213)978-3-030-28790-0 035 $a(PPN)242818803 035 $a(EXLCZ)994100000010013750 100 $a20191213d2019 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aFinite Form Representations for Meijer G and Fox H Functions $eApplied to Multivariate Likelihood Ratio Tests Using Mathematica®, MAXIMA and R /$fby Carlos A. Coelho, Barry C. Arnold 205 $a1st ed. 2019. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2019. 215 $a1 online resource (xviii, 515 pages) 225 1 $aLecture Notes in Statistics,$x2197-7186 ;$v223 311 08$a3-030-28789-0 327 $aPreface -- 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. 330 $aThis book depicts a wide range of situations in which there exist finite form representations for the Meijer G and the Fox H functions. Accordingly, it will be of interest to researchers and graduate students who, when implementing likelihood ratio tests in multivariate analysis, would like to know if there exists an explicit manageable finite form for the distribution of the test statistics. In these cases, both the exact quantiles and the exact p-values of the likelihood ratio tests can be computed quickly and efficiently. The test statistics in question range from common ones, such as those used to test e.g. the equality of means or the independence of blocks of variables in real or complex normally distributed random vectors; to far more elaborate tests on the structure of covariance matrices and equality of mean vectors. The book also provides computational modules in Mathematica®, MAXIMA and R, which allow readers to easily implement, plot and compute the distributions of any of these statistics, or any other statistics that fit into the general paradigm described here. 410 0$aLecture Notes in Statistics,$x2197-7186 ;$v223 606 $aStatistics 606 $aMathematical statistics$xData processing 606 $aStatistics 606 $aStatistical Theory and Methods 606 $aStatistics and Computing 606 $aApplied Statistics 615 0$aStatistics. 615 0$aMathematical statistics$xData processing. 615 0$aStatistics. 615 14$aStatistical Theory and Methods. 615 24$aStatistics and Computing. 615 24$aApplied Statistics. 676 $a519.5 676 $a519.24 (edition:23) 700 $aCoelho$b Carlos A$4aut$4http://id.loc.gov/vocabulary/relators/aut$0781327 702 $aArnold$b Barry C$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910364956003321 996 $aFinite Form Representations for Meijer G and Fox H Functions$92517207 997 $aUNINA