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

Benjamin Reiser; Irwin Guttman

doi:10.1016/0167-9473(87)90008-9

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

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

Abstract

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 language	English
Pages (from-to)	59-66
Number of pages	8
Journal	Computational Statistics and Data Analysis
Volume	5
Issue number	1
DOIs	https://doi.org/10.1016/0167-9473(87)90008-9
State	Published - 1987
Externally published	Yes

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.

Keywords

Maximum likelihood
Predictive
Reliability
UMVUE

ASJC Scopus subject areas

Statistics and Probability
Computational Mathematics
Computational Theory and Mathematics
Applied Mathematics

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10.1016/0167-9473(87)90008-9

Cite this

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

abstract = "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.",

keywords = "Maximum likelihood, Predictive, Reliability, UMVUE",

author = "Benjamin Reiser and Irwin Guttman",

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.",

year = "1987",

doi = "10.1016/0167-9473(87)90008-9",

language = "English",

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AU - Guttman, Irwin

N1 - 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.

PY - 1987

Y1 - 1987

N2 - 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.

AB - 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.

KW - Maximum likelihood

KW - Predictive

KW - Reliability

KW - UMVUE

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JF - Computational Statistics and Data Analysis

IS - 1

ER -

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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