A Gaussian Approximation to the Distribution of Definite Quadratic Form.
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 11, 1971
- Accession Number
- AD0737617
Entities
People
- D. R. Jensen
- Herbert Solomon
Organizations
- Stanford University