Accession Number : AD0266122

Title :   AN APPROXIMATION TO THE PROBABILITY INTEGRAL OF THE GAMMA DISTRIBUTION

Corporate Author : RUTGERS - THE STATE UNIV NEW BRUNSWICK N J

Personal Author(s) : PINKHAM,ROGER S.

Report Date : SEP 1961

Pagination or Media Count : 1

Abstract : Consider a solid cube C of side 2x in n-space and a solid ball B of radius R. B and C are each centered at the origin, and R and x are so chosen as to yield the same volume. Let f be the unit, spherically sym etric normal in n-space centered at the origin. The integral of (f dv) around C is less than the integral of (f dv) around B, where the integrals are multiple and dv denotes the cartesian volume element in nspace. An examination shows that nowhere is the integral nature of n vital; so the geometric picture is sacrificed and the fractional n is considered. This yields an approximation for the probability integral of the gamma distribution for small values of the shape parameter. Numerical details are presented which show the approximation to be good.

Descriptors :   *INTEGRAL EQUATIONS, *STATISTICAL DISTRIBUTIONS, ANALYTIC GEOMETRY, FUNCTIONS(MATHEMATICS), NUMERICAL ANALYSIS, PROBABILITY, TABLES(DATA)

Distribution Statement : APPROVED FOR PUBLIC RELEASE