
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 noncentral chisquare 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 chisquare 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