Investigation of polynomial normal transform

Xingyuan Chen, Yeou-Koung Tung*

*Corresponding author for this work

Research output: Contribution to journalArticle

62 Scopus citations


Normal transformation is often used in probabilistic analysis especially when multivariate non-normal random variables are involved. A third-order polynomial normal transformation technique is presented in this paper and its characteristics examined. Four methods based on different statistical information of a random variable are used to determine the polynomial coefficients in this normal transformation technique. The performance of these four methods is investigated by comparing with parametric technique using Rosenblatt transformation that preserves the marginal distribution of a non-normal random variable. From the numerical experiment conducted, this simple technique is found to be quite accurate, and it is less restrictive in its usage for merely requiring the information of the first four statistical moments of a random variable rather than requiring a stronger assumption of the full distribution information in the Rosenblatt transformation. The technique is especially attractive when only samples of the random variables are available.

Original languageEnglish
Pages (from-to)423-445
Number of pages23
JournalStructural Safety
Issue number4
StatePublished - 1 Jan 2003


  • Fisher-Cornish asymptotic expansion
  • L-moments
  • Least-square
  • Multivariate distribution model
  • Normal transformation
  • Product moments
  • Random variable
  • Third-order polynomial normal transformation

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