The existence of the first negative moment

Walter W. Piegorsch, George Casella

Research output: Contribution to journalArticlepeer-review

28 Scopus citations


The question of the existence of negative moments of a continuous probability density function is explored. A sufficient condition for the existence of the first negative moment is given. The condition is easy to verify, as it involves limits rather than integrals. An example is given, however, that shows that this simple condition is not necessary for the existence of the first negative moment. The delicacy of the characterization of existence is explored further with some results concerning the existence of moments surrounding the first negative moment.

Original languageEnglish (US)
Pages (from-to)60-62
Number of pages3
JournalAmerican Statistician
Issue number1
StatePublished - Feb 1985


  • Inverse moment
  • Limit conditions
  • Sufficient conditions

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Statistics, Probability and Uncertainty


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