Mono tonicity of a power function: An elementary probabilistic proof

David Gilat*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


It is pointed out that in many one-sided testing situations for a real-valued parameter 6, the monotonicity of the power function hinges on the stochastic order of the underlying family of distributions [Fθ] rather than on the stronger property of monotone likelihood ratio of the family. An elementary proof, accessible to students of introductory probability and statistics, is presented.

Original languageEnglish
Pages (from-to)91-93
Number of pages3
JournalAmerican Statistician
Issue number2
StatePublished - May 1977
Externally publishedYes


  • Distributions with given marginals
  • Power function
  • Stochastic order
  • Sums of independent random variables


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