Deriving generalized means as least squares and maximum likelihood estimates

Roger L. Berger

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


Functions called generalized means are of interest in statistics because they are simple to compute, have intuitive appeal, and can serve as reasonable parameter estimates. The well-known arithmetic, geometric, and harmonic means are all examples of generalized means. We show how generalized means can be derived in a unified way, as least squares estimates for a transformed data set. We also investigate models that have generalized means as their maximum likelihood estimates.

Original languageEnglish (US)
Pages (from-to)276-278
Number of pages3
JournalAmerican Statistician
Issue number4
StatePublished - Nov 1992
Externally publishedYes


  • Arithmetic mean
  • Exponential family
  • Geometric mean
  • Harmonic mean

ASJC Scopus subject areas

  • Statistics and Probability
  • General Mathematics
  • Statistics, Probability and Uncertainty


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