A note on the transformation of chi-squared variables to normality

Douglas M. Hawkins, R. A J Wixley

Research output: Contribution to journalArticlepeer-review

48 Scopus citations


It is shown that the fourth root of a chi-squared distributed random variable has a distribution that is very close to normal for all degrees of freedom. The parameters of the approximating normal distribution are given exactly in terms of the gamma function, and a simpler approximation involving only square and fourth roots of functions of the number of degrees of freedom is also given. © 1986 American Statistical Association.

Original languageEnglish (US)
Pages (from-to)296-298
Number of pages3
JournalAmerican Statistician
Issue number4
StatePublished - 1986


  • Box-Cox transformation
  • Chi-squared distribution
  • Normal distribution


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