A new chi-square approximation to the distribution of non-negative definite quadratic forms in non-central normal variables

Huan Liu, Yongqiang Tang, Hao Helen Zhang

Research output: Contribution to journalArticle

121 Scopus citations

Abstract

This note proposes a new chi-square approximation to the distribution of non-negative definite quadratic forms in non-central normal variables. The unknown parameters are determined by the first four cumulants of the quadratic forms. The proposed method is compared with Pearson's three-moment central χ2 approximation approach, by means of numerical examples. Our method yields a better approximation to the distribution of the non-central quadratic forms than Pearson's method, particularly in the upper tail of the quadratic form, the tail most often needed in practical work.

Original languageEnglish (US)
Pages (from-to)853-856
Number of pages4
JournalComputational Statistics and Data Analysis
Volume53
Issue number4
DOIs
StatePublished - Feb 15 2009

ASJC Scopus subject areas

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics

Fingerprint Dive into the research topics of 'A new chi-square approximation to the distribution of non-negative definite quadratic forms in non-central normal variables'. Together they form a unique fingerprint.

  • Cite this