Statistical inference for pr(y < x): The normal case

Benjamin Reiser, Irwin Guttman

Research output: Contribution to journalArticlepeer-review


This article examines statistical inference for Pr(Y < X), where X and Y are independent normal variates with unknown means and variances. The case of unequal variances is stressed. X can be interpreted as the strength of a component subjected to a stress Y, and Pr(Y < X) is the component’s reliability. Two approximate methods for obtaining confidence intervals and an approximate Bayesian probability interval are obtained. The actual coverage probabilities of these intervals are examined by simulation.

Original languageEnglish
Pages (from-to)253-257
Number of pages5
Issue number3
StatePublished - Aug 1986

Bibliographical note

Funding Information:
We would like to thank the editor and the referees for their helpful comments on an earlier version of this article. Preparation of this article was sponsored by U.S. Army-Contract DAAG-29-80-C&I41 and Natural Sciencesa nd Engineering Research Council (Canada) Grant A8743.


  • Bayesian and sampling theory
  • Interval estimators
  • Maximum likelihood
  • Reliability

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics


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