Convergent series expressions for inverse moments of quadratic forms in normal variables

Murray D. Smith

doi:10.1111/j.1467-842X.1988.tb00854.x

Convergent series expressions for inverse moments of quadratic forms in normal variables

Murray D. Smith^*

^*Corresponding author for this work

University of Sydney

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

Using relatively recent results from multivariate distribution theory, a direct approach to evaluating the inverse moments of a quadratic form in normal variables is proposed. Convergent infinite series expressions involving the invariant polynomials of matrix argument are obtained. The solution also depends upon a positive scalar which is arbitrarily chosen. For the solution to converge an upper bound upon this scalar is derived.

Original language	English
Pages (from-to)	235-246
Number of pages	12
Journal	Australian Journal of Statistics
Volume	30
Issue number	2
DOIs	https://doi.org/10.1111/j.1467-842X.1988.tb00854.x
Publication status	Published - 01 Jun 1988
Externally published	Yes

Keywords

invariant polynomials
inverse moments
Quadratic forms
zonal polynomials

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10.1111/j.1467-842X.1988.tb00854.x

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AB - Using relatively recent results from multivariate distribution theory, a direct approach to evaluating the inverse moments of a quadratic form in normal variables is proposed. Convergent infinite series expressions involving the invariant polynomials of matrix argument are obtained. The solution also depends upon a positive scalar which is arbitrarily chosen. For the solution to converge an upper bound upon this scalar is derived.

KW - invariant polynomials

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KW - Quadratic forms

KW - zonal polynomials

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Convergent series expressions for inverse moments of quadratic forms in normal variables

Abstract

Keywords

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