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


Full Text : http://www.dtic.mil/get-tr-doc/pdf?AD=AD0600972


Report Date : APR 1964


Pagination or Media Count : 19


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 Nicholson's 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 u's and v's 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