AN APPROXIMATION TO THE PROBABILITY INTEGRAL OF THE GAMMA DISTRIBUTION
RUTGERS - THE STATE UNIV NEW BRUNSWICK N J
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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.