Computing the noncentral beta distribution with S-system.
type: Item
instance of: scholarly article
title: Computing the noncentral beta distribution with S-system.
zbMATH Open document ID: 1061.62513
DOI: 10.1016/S0167-9473(99)00067-5
author: N. Delaunay
published in: Computational Statistics and Data Analysis
publication date: 2000-08-21T00:00:00Z
review text: Based on the recasting techniques of \textit{P. F. Rust} and \textit{E. O. Voit} [J. Stat. Computat. Simulation 42, No. 3--4, 187--249 (1992); Biom J. 32, 681--695 (1990; Zbl 0716.62027); J. Am. Stat. Assoc. 85, 572--578 (1990)], an S-system form of the noncentral beta distribution is extended from that of the noncentral F distribution and the other one is newly derived. The computing methods of this distribution have received much attention during the last decade. Its cumulative probabilities, densities, quantiles and related distributional values can be calculated in one \(S\)-system form. We demonstrate the new computational results using the \(S\)-system numerical solver ESSYNS. Consistent results are obtained from these two \(S\)-system forms under various situations. In addition, we compare the performance with an ad hoc computing method by evaluating the cumulative probabilities and densities jointly. The S-system formulation provides significant numerical advantages over its original form. Further properties are also discussed.
Mathematics Subject Classification ID: 62E15
Mathematics Subject Classification ID: 65C60
zbMATH DE Number: 1493275
zbMATH Keywords: Statistical computing
zbMATH Keywords: Differential equation
zbMATH Keywords: Recasting
zbMATH Keywords: Power law
zbMATH Keywords: Taylor series
describes a project that uses: AS 226
describes a project that uses: ESSYNS
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1493275