Accession Number:

AD0600972

Title:

RATIOS OF NORMAL VARIABLES AND RATIOS OF SUMS OF UNIFORM VARIABLES

Descriptive Note:

Mathematics research

Corporate Author:

BOEING SCIENTIFIC RESEARCH LABS SEATTLE WA

Personal Author(s):

• Marsaglia, George

Report Date:

1964-04-01

Pagination or Media Count:

19.0

Abstract:

The principal part of this paper is devoted to the study of the distribution and density functions of the ratio of two normal random variables. It gives several representations of the distribution function in terms of the bivariate normal distribution and Nicholsons V function, both of which have been extensively studied, and for which tables and computational procedures are readily available. One of these representations leads to an easy derivation of the density function in terms of the Cauchy density and the normal density and integral. A number of graphs of the possible shapes of the density are given, together with an indication of when the density is unimodal or bimodal. The last part of the paper discusses the distribution of the ratio u sub 1 . . . u sub n V sub 1 . . . V sub m where the us and vs are independent, uniform variables. The exact distribution for all n and m is given, and some approximations discussed.

Descriptors:

• *STATISTICAL DISTRIBUTIONS
• *STATISTICAL FUNCTIONS
• *NUMBER THEORY
• DENSITY
• INTEGRALS
• DISTRIBUTION THEORY
• FUNCTIONS(MATHEMATICS)
• MATHEMATICAL LOGIC

Subject Categories:

• Statistics and Probability

Distribution Statement:

APPROVED FOR PUBLIC RELEASE