The DOI matches its Crossref record; 11 of the 12 references it cites were found in a registry or an index, and 1 are not checked yet.
Multivariate Normal Probabilities: Implementing an Old Idea of Plackett's
Abstract
This article describes a reduction formula for the computation of multivariate normal probabilities first developed by Plackett. The method is recursive and, despite very promising results, seems not to have been implemented before. Extensive numerical results are given to compare the effectiveness of the approach to other methods from the literature.
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Cites
Stroud, A. H., & Secrest, D. (1966) · Cited by 1,391
Numerical Computation of Multivariate Normal Probabilities
Genz, A. (1992) · Journal of Computational and Graphical Statistics · doi:10.1080/10618600.1992.10477010 · Cited by 1,020
The One-Sided Barrier Problem for Gaussian Noise
Slepian, D. (1962) · Bell System Technical Journal · doi:10.1002/j.1538-7305.1962.tb02419.x · Cited by 784
The Multivariate Normal Distribution
Izenman, A. J., & Tong, Y. L. (1991) · Technometrics · doi:10.1080/00401706.1991.10484897 · Cited by 662
Numerical Computation of Multivariate Normal Probabilities
Genz, A. C. (1992) · Journal of Computational and Graphical Statistics · doi:10.2307/1390838 · Cited by 293
A REDUCTION FORMULA FOR NORMAL MULTIVARIATE INTEGRALS
PLACKETT, R. L. (1954) · Biometrika · doi:10.1093/biomet/41.3-4.351 · Cited by 273
Algorithm AS 195: Multivariate Normal Probabilities with Error Bound
Schervish, M. J. (1984) · Applied Statistics · doi:10.2307/2347670 · Cited by 265
A reduction formula for normal multivariate integrals
Plackett, R. L. (1954) · Biometrika · doi:10.2307/2332716 · Cited by 262
Generating Correlation Matrices
Marsaglia, G., & Olkin, I. (1984) · SIAM Journal on Scientific and Statistical Computing · doi:10.1137/0905034 · Cited by 108
Computation of the trivariate normal integral
Drezner, Z. (1994) · Mathematics of Computation · doi:10.1090/s0025-5718-1994-1185242-8 · Cited by 40
Research works printed but not linked: 1
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Cited by
The Normal Law Under Linear Restrictions: Simulation and Estimation via Minimax Tilting
Botev, Z. I. (2017) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/rssb.12162 · Cited by 247
Bayesian Conjugacy in Probit, Tobit, Multinomial Probit and Extensions: A Review and New Results
Anceschi, N., Fasano, A., Durante, D., & Zanella, G. (2023) · Journal of the American Statistical Association · doi:10.1080/01621459.2023.2169150 · Cited by 27
On numerical calculation of probabilities according to Dirichlet distribution
Gouda, A. A., & Szántai, T. (2009) · Annals of Operations Research · doi:10.1007/s10479-009-0601-9 · Cited by 19
Estimation of multivariate probit models by exact maximum likelihoodPreprint
Huguenin, J., Pelgrin, F., & Holly, A. (2009) · RePEc: Research Papers in Economics · Cited by 12
Calculation of orthant probabilities by the holonomic gradient method
Koyama, T., & Akimichi Takemura, Y. (2015) · Japan Journal of Industrial and Applied Mathematics · doi:10.1007/s13160-015-0166-8 · Cited by 11
Metadata
- Authors
- Gassmann, H. I.
- Affiliations
- Dalhousie University (CA)
- Corresponding author
- Gassmann, H. I
- Venue
- Journal of Computational and Graphical Statistics
- Publisher
- Informa UK Limited
- Published
- 2003-09
- Volume
- 12
- Issue
- 3
- Pages
- 731-752
- ISSN
- 1061-8600 (ISSN-L)
- 1537-2715
- OpenAlex
- W2165084744
- Cited by
- 11
- References
- 10
- Citations by year
- 2025: 1 · 2023: 1 · 2018: 1 · 2017: 1 · 2016: 2 · 2015: 1 · 2014: 1
- FWCI
- 0.31
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Computational and Graphical Statistics (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Physical Sciences › Mathematics › Applied Mathematics › Mathematical functions and polynomials
- Keywords
- multivariate normal probabilities, recursive computation, numerical integration, multivariate normal distribution
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- CoChat. (2026). Citation check: Multivariate Normal Probabilities: Implementing an Old Idea of Plackett's. https://app.cochat.ai/papers/10.1198/1061860032283
- The paper
- Gassmann, H. I. (2003). Multivariate Normal Probabilities: Implementing an Old Idea of Plackett's. Journal of Computational and Graphical Statistics. https://doi.org/10.1198/1061860032283
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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