The Annals of Mathematical Statistics

Distribution of Definite and of Indefinite Quadratic Forms

John Gurland

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Abstract

A previous paper [1] has given a method of approximating the distribution of a quadratic form in normally distributed variables by means of convergent Laguerrian expansions. In the case of an indefinite quadratic form, however, the method was restrictive in that it might be difficult to obtain the semi-moments required in computing the coefficients of the expansion. The present article circumvents this difficulty for positive values of the argument of the distribution function, when the number of positive or the number of negative eigenvalues is even, and also yields convergent expansions for the distribution function involving Laguerre polynomials. The proposed method has the further advantage that no moments or semi-moments need be calculated.

Article information

Source
Ann. Math. Statist., Volume 26, Number 1 (1955), 122-127.

Dates
First available in Project Euclid: 28 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoms/1177728600

Digital Object Identifier
doi:10.1214/aoms/1177728600

Mathematical Reviews number (MathSciNet)
MR67417

Zentralblatt MATH identifier
0064.12902

JSTOR
links.jstor.org

Citation

Gurland, John. Distribution of Definite and of Indefinite Quadratic Forms. Ann. Math. Statist. 26 (1955), no. 1, 122--127. doi:10.1214/aoms/1177728600. https://projecteuclid.org/euclid.aoms/1177728600


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Corrections

  • See Correction: John Gurland. Correction Notes: Correction to "Distribution of Definite and of Indefinite Quadratic Forms". Ann. Math. Statist., Volume 33, Number 2 (1962), 813--813.