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

Murray D. Smith*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Pages (from-to)235-246
Number of pages12
JournalAustralian Journal of Statistics
Volume30
Issue number2
DOIs
Publication statusPublished - 01 Jun 1988
Externally publishedYes

Keywords

  • invariant polynomials
  • inverse moments
  • Quadratic forms
  • zonal polynomials

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