Computation of tolerance ellipses for bivariate and trivariate normal populations
Computation of tolerance ellipses for bivariate and trivariate normal populations
We consider the computation of the critical constants c of a p-content (1-\alpha)-confidence tolerance ellipse for bivariate and trivariate normal populations which are probably the most used multivariate normal distributions in applications. There are only approximation methods available in the statistical literature for computing $c$. Without knowing the accurate value of c, it is impossible to assess the accuracy of the approximation methods. In this paper, a new method is given to compute $c$. Although the method is also based on Monte-Carlo simulation, it allows $c$ to be computed as accurate as required if the number of simulation replications is sufficiently large. The R codes provided allow easy implementation of the method. Furthermore, the method allows the accuracy of the available approximation methods for bivariate and trivariate normal distributions to be assessed.
Monte-Carlo simulation, Multivariate normal distribution, tolerance regions
3630-3638
Liu, Wei
b64150aa-d935-4209-804d-24c1b97e024a
Bretz, F.
51270819-e491-4a72-a410-679d86231e64
Hayter, Anthony
841aec34-bd38-42bb-974c-e3de4752ac38
Kiatsupaibul, S.
b072063d-4be1-4ca0-8d4f-27740f0fa651
22 November 2022
Liu, Wei
b64150aa-d935-4209-804d-24c1b97e024a
Bretz, F.
51270819-e491-4a72-a410-679d86231e64
Hayter, Anthony
841aec34-bd38-42bb-974c-e3de4752ac38
Kiatsupaibul, S.
b072063d-4be1-4ca0-8d4f-27740f0fa651
Liu, Wei, Bretz, F., Hayter, Anthony and Kiatsupaibul, S.
(2022)
Computation of tolerance ellipses for bivariate and trivariate normal populations.
Journal of Statistical Computation and Simulation, 92 (17), .
(doi:10.1080/00949655.2022.2076091).
Abstract
We consider the computation of the critical constants c of a p-content (1-\alpha)-confidence tolerance ellipse for bivariate and trivariate normal populations which are probably the most used multivariate normal distributions in applications. There are only approximation methods available in the statistical literature for computing $c$. Without knowing the accurate value of c, it is impossible to assess the accuracy of the approximation methods. In this paper, a new method is given to compute $c$. Although the method is also based on Monte-Carlo simulation, it allows $c$ to be computed as accurate as required if the number of simulation replications is sufficiently large. The R codes provided allow easy implementation of the method. Furthermore, the method allows the accuracy of the available approximation methods for bivariate and trivariate normal distributions to be assessed.
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pp5
- Accepted Manuscript
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00949655.2022
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More information
Accepted/In Press date: 7 May 2022
e-pub ahead of print date: 27 June 2022
Published date: 22 November 2022
Additional Information:
Funding Information:
We thank the two anonymous referees for very helpful comments and suggestions.
Publisher Copyright:
© 2022 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.
Keywords:
Monte-Carlo simulation, Multivariate normal distribution, tolerance regions
Identifiers
Local EPrints ID: 457330
URI: http://eprints.soton.ac.uk/id/eprint/457330
ISSN: 0094-9655
PURE UUID: 1b85f8c2-dc0b-4411-bf45-48805cc543f3
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Date deposited: 01 Jun 2022 16:41
Last modified: 17 Mar 2024 07:18
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Contributors
Author:
F. Bretz
Author:
Anthony Hayter
Author:
S. Kiatsupaibul
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