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

Benjamin Reiser; Irwin Guttman

doi:10.1080/00401706.1986.10488133

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

Benjamin Reiser, Irwin Guttman

Department of Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	253-257
Number of pages	5
Journal	Technometrics
Volume	28
Issue number	3
DOIs	https://doi.org/10.1080/00401706.1986.10488133
State	Published - 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.

Keywords

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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10.1080/00401706.1986.10488133

Cite this

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title = "Statistical inference for pr(y < x): The normal case",

abstract = "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{\textquoteright}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.",

keywords = "Bayesian and sampling theory, Interval estimators, Maximum likelihood, Reliability",

author = "Benjamin Reiser and Irwin Guttman",

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.",

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AU - Guttman, Irwin

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N2 - 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.

AB - 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.

KW - Bayesian and sampling theory

KW - Interval estimators

KW - Maximum likelihood

KW - Reliability

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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