Open Access
March, 1955 Note on the Distribution of a Definite Quadratic Form
James Pachares
Ann. Math. Statist. 26(1): 128-131 (March, 1955). DOI: 10.1214/aoms/1177728601


An expression is derived for the distribution of a definite quadratic form in independent $N(0, 1)$ variates which depends only on the value of the determinant of the form and on the moments of a quadratic form whose matrix is the inverse of the original quadratic form. This expression is an alternating series which converges absolutely and is such that if we stop with any even power of the series we have an upper bound and if we stop with any odd power of the series a lower bound to the cumulative distribution function. The result given in this note seems to be in several ways an improvement over the method given in Robbins [2].


Download Citation

James Pachares. "Note on the Distribution of a Definite Quadratic Form." Ann. Math. Statist. 26 (1) 128 - 131, March, 1955.


Published: March, 1955
First available in Project Euclid: 28 April 2007

zbMATH: 0064.12903
MathSciNet: MR67416
Digital Object Identifier: 10.1214/aoms/1177728601

Rights: Copyright © 1955 Institute of Mathematical Statistics

Vol.26 • No. 1 • March, 1955
Back to Top