A comparison of three point estimators for P(Y < X) in the normal case

Benjamin Reiser, Irwin Guttman

Research output: Contribution to journalArticlepeer-review


This paper discusses point estimation for R = P(Y < X) where X and Y are independent normal variables. R can be considered to be the reliability of a system with strength X to which is applied stress Y. A predictive estimator which can be calculated from the Behrens-Fisher distribution is derived and compared with the maximum likelihood and uniformly minimum variance unbiased estimators through a simulation study.

Original languageEnglish
Pages (from-to)59-66
Number of pages8
JournalComputational Statistics and Data Analysis
Issue number1
StatePublished - 1987
Externally publishedYes

Bibliographical note

Funding Information:
The authorsw ould like to acknowledgwe ith thanks commentsm adeby an associatee ditora nd two referees. This work partiallys upportedb y NSERC of Canada,u nderg rantN o. A8743, and by the MathematicRs esearchC enter,U niversityo f Wisconsin( Madison) underg rantsD AAG 29-80-C-004a1 nd DAAG29-80-C-0013.


  • Maximum likelihood
  • Predictive
  • Reliability

ASJC Scopus subject areas

  • Statistics and Probability
  • Computational Mathematics
  • Computational Theory and Mathematics
  • Applied Mathematics


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