Current Volume | Browse | Search | RSSHome | Instructions for Authors | JSS Style Guide | Editorial Board

Authors: George Marsaglia
Title: [download]
(13474)
Ratios of Normal Variables
Reference: Vol. 16, Issue 4, May 2006
Submitted 2006-03-07, Accepted 2006-05-11
Type: Article
Abstract:

This article extends and amplifies on results from a paper of over forty years ago. It provides software for evaluating the density and distribution functions of the ratio z/w for any two jointly normal variates z,w, and provides details on methods for transforming a general ratio z/w into a standard form, (a+x)/(b+y) , with x and y independent standard normal and a, b non-negative constants. It discusses handling general ratios when, in theory, none of the moments exist yet practical considerations suggest there should be approximations whose adequacy can be verified by means of the included software. These approximations show that many of the ratios of normal variates encountered in practice can themselves be taken as normally distributed. A practical rule is developed: If a < 2.256 and 4 < b then the ratio (a+x)/(b+y) is itself approximately normally distributed with mean μ = a/(1.01b - .2713) and variance σ2 = (a2 + 1)/(b2 + .108b - 3.795) μ2.

Paper: [download]
(13474)
Ratios of Normal Variables
(application/pdf, 272.9 KB)
Supplements: [download]
(1222)
zoverw.c: Sample C routines
(application/zip, 2.6 KB)
Resources: BibTeX | OAI
Creative Commons License
This work is licensed under the licenses
Paper: Creative Commons Attribution 3.0 Unported License
Code: GNU General Public License (at least one of version 2 or version 3)
Current Volume | Browse | Search | RSSHome | Instructions for Authors | JSS Style Guide | Editorial Board