Accession Number : AD0737617

Title :   A Gaussian Approximation to the Distribution of Definite Quadratic Form.

Descriptive Note : Technical rept.,

Corporate Author : STANFORD UNIV CALIF DEPT OF STATISTICS

Personal Author(s) : Jensen,D. R. ; Solomon,Herbert

Report Date : 11 NOV 1971

Pagination or Media Count : 28

Abstract : Let Q sub K = summation from j = 1 to K of c sub j (x sub j + a sub j) squared be a definite quadratic form in independent standardized Gaussian variables, x sub j, and let Q sub k = theta sub 1 be its mean. The normalizing transformation (Q sub k/theta sub 1) sup h is investigated, where h is determined by the first three moments of Q sub k. In particular, a new Gaussian approximation to the non-central chi-square distribution is found for which the coefficient of skewness is smaller, by an order of magnitude, than a cube root transformation presently in the literature. The transformation further specializes to the classical cube root transformation of Wilson and Hilferty for the central chi-square distribution. The proposed approximation is simple to apply, and it compares well with several other approximations in a number of cases studied numerically. (Author)

Descriptors :   (*STATISTICAL PROCESSES, APPROXIMATION(MATHEMATICS)), STATISTICAL TESTS, STOCHASTIC PROCESSES, PROBABILITY DENSITY FUNCTIONS, TABLES(DATA)

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE