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^*

^*Awdur cyfatebol y gwaith hwn

The University of Sydney

Allbwn ymchwil: Cyfraniad at gyfnodolyn › Erthygl › adolygiad gan gymheiriaid

3 Dyfyniadau (Scopus)

Crynodeb

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.

Iaith wreiddiol	Saesneg
Tudalennau (o-i)	235-246
Nifer y tudalennau	12
Cyfnodolyn	Australian Journal of Statistics
Cyfrol	30
Rhif cyhoeddi	2
Dynodwyr Gwrthrych Digidol (DOIs)	https://doi.org/10.1111/j.1467-842X.1988.tb00854.x
Statws	Cyhoeddwyd - 01 Meh 1988
Cyhoeddwyd yn allanol	Ie

Mynediad at Ddogfen

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

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Dolen barhaus

Ffeiliau eraill a chysylltiadau

Dolen i’r cyhoeddiad yn Scopus

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title = "Convergent series expressions for inverse moments of quadratic forms in normal variables",

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.",

keywords = "invariant polynomials, inverse moments, Quadratic forms, zonal polynomials",

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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

KW - inverse moments

KW - Quadratic forms

KW - zonal polynomials

UR - https://www.scopus.com/pages/publications/84985634197

U2 - 10.1111/j.1467-842X.1988.tb00854.x

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

M3 - Article

AN - SCOPUS:84985634197

SN - 1026-597X

VL - 30

SP - 235

EP - 246

JO - Australian Journal of Statistics

JF - Australian Journal of Statistics

IS - 2

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

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Ffeiliau eraill a chysylltiadau

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