On the expectation of a ratio of quadratic forms in normal variables

Murray D. Smith*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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Abstract

Using relatively recent results from multivariate distribution theory, the expectation of a ratio of quadratic forms in normal variables is obtained. Infinite series expressions involving the invariant polynomials of matrix argument are derived. Convergence of the solution depends upon the choice made for two positive, but upper bounded, constants. The same methodology is used to obtain the expectation of multiple ratios of quadratic forms in normal variables.

Original languageEnglish
Pages (from-to)244-257
Number of pages14
JournalJournal of Multivariate Analysis
Volume31
Issue number2
DOIs
Publication statusPublished - 01 Nov 1989
Externally publishedYes

Keywords

  • generalized hypergeometric function
  • invariant polynomials
  • quadratic forms
  • zonal polynomials

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