Accession Number : AD0420434

Title :   THE DOUBLY NON-CENTRAL F-DISTRIBUTION EXPRESSED IN FINITE TERMS,

Corporate Author : MASSACHUSETTS INST OF TECH LEXINGTON LINCOLN LAB

Personal Author(s) : Price,Robert

Report Date : 13 SEP 1963

Pagination or Media Count : 56

Abstract : There is an attempt to provide new, explicit and exact formulas for the doubly non-central F-distribution, defined as the cumulative distribution function, where the numbers of degrees of freedom of the chi-square variates need not be equal, but are restricted to be either both even or both odd. The formula for the even-even case is considerably simpler in structure than that for the odd-odd case, although the former involves Bessel functions where the latter contains error-functions. Therefore, at least for high degree-numbers it may be more convenient to try interpolation (between the degree-numbers) on numerical results obtained from the even-even formula when dealing with odd-odd cases, than to use the odd-odd formula directly. Mixed cases, where one degree-number is even and the other is odd, do not at present appear susceptible of analysis, so that here interpolation offers the only hope short of literal numerical integration. (Author)

Descriptors :   (*STATISTICAL FUNCTIONS, STATISTICAL ANALYSIS), SERIES(MATHEMATICS), FUNCTIONS(MATHEMATICS), SPECIAL FUNCTIONS (MATHEMATICAL), BESSEL FUNCTIONS, PROBABILITY, NUMERICAL INTEGRATION, INTEGRALS, EQUATIONS, COMBINATORIAL ANALYSIS

Distribution Statement : APPROVED FOR PUBLIC RELEASE