Improving the numerical technique for computing the accumulated distribution of a quadratic form in normal variables

Zeng-Hua Lu, Maxwell L King

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12 Citations (Scopus)


This paper is concerned with the technique of numerically evaluating the cumulative distribution function of a quadratic form in normal variables. The efficiency of two new truncation bounds and all existing truncation bounds are investigated. We also find that the suggestion in the literature for further splitting truncation errors might reduce computational efficiency, and the optimum splitting rate could be different in different situations. A practical solution is provided. The paper also discusses a modified secant algorithm for finding the critical value of the distribution at any given significance level.

Original languageEnglish
Pages (from-to)149-165
Number of pages17
JournalEconometric Reviews
Issue number2
Publication statusPublished - 2002


  • C19
  • C63
  • JEL Classification
  • Newton'
  • Numerical inversion of characteristic function
  • Quadratic form in normal variables
  • s method
  • Secant method
  • Truncation error

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