Moments of the truncated normal distribution

Research output: Contribution to journalArticlepeer-review

32 Scopus citations


The truncated (below zero) normal distribution is considered. Some existing results are surveyed, and a recursive moment formula is used to derive the first four central moments in terms of the mean and variance of the underlying normal and in terms of lower moments of the truncated distribution. Bounding and monotonicity of the moments of the truncated distribution are considered and some previously unknown features of the distribution are presented. Moment results are used to derive a test of the distributional form. The distribution is commonly used in economics, particularly in the stochastic frontier literature. Application to the stochastic frontier model is briefly considered.

Original languageEnglish (US)
Pages (from-to)133-138
Number of pages6
JournalJournal of Productivity Analysis
Issue number2
StatePublished - Apr 2015


  • Moments
  • Probability
  • Stochastic frontier model

ASJC Scopus subject areas

  • Business and International Management
  • Social Sciences (miscellaneous)
  • Economics and Econometrics


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