The DOI matches its Crossref record; 8 of the 8 references it cites were found in a registry or an index.
A REDUCTION FORMULA FOR NORMAL MULTIVARIATE INTEGRALS
Abstract
A REDUCTION FORMULA FOR NORMAL MULTIVARIATE INTEGRALS Get access R. L. PLACKETT R. L. PLACKETT University of Liverpool Search for other works by this author on: Oxford Academic Google Scholar Biometrika, Volume 41, Issue 3-4, 3 December 1954, Pages 351–360, https://doi.org/10.1093/biomet/41.3-4.351 Published: 03 December 1954
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In the citing paper
“It satisfies Plackett's identity exactly or approximately, depending on the correlation parameter being differentiated.”
From A limit formula and recursive algorithm for multivariate Normal tail probability (2025) · cites this paper as Plackett (1954)
In the citing paper
“Plackett's idenity (Plackett, 1954) says that ∂P (X ≥ u)/∂C ij = ∂ 2 P (X ≥ u)/∂u i ∂u j for any i ̸ = j.”
From A limit formula and recursive algorithm for multivariate Normal tail probability (2025) · cites this paper as Plackett, 1954
Citations
Cites
Methods of Mathematical Physics
Courant, R., & Hilbert, D. (1989) · Wiley eBooks · doi:10.1002/9783527617210 · Cited by 8,067
Quantal Responses to Mixtures of Poisons
Plackett, R. L., & Hewlett, P. S. (1952) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.2517-6161.1952.tb00108.x · Cited by 206
Self-citationON THE MOMENTS OF ORDER STATISTICS IN SAMPLES FROM NORMAL POPULATIONS
Ruben, H. (1954) · Biometrika · doi:10.1093/biomet/41.1-2.200 · Cited by 112
Rank Correlation and Product-Moment Correlation
Moran, P. A. P. (1948) · Biometrika · doi:10.1093/biomet/35.1-2.203 · Cited by 102
A Note on the Evaluation of the Multivariate Normal Integral
David, F. N. (1953) · Biometrika · doi:10.1093/biomet/40.3-4.458 · Cited by 89
THE FUNCTIONS OF SCHLÄFLI AND LOBATSCHEFSKY
Coxeter, H. S. M. (1935) · The Quarterly Journal of Mathematics · doi:10.1093/qmath/os-6.1.13 · Cited by 86
ON THE RANGE OF PARTIAL SUMS OF A FINITE NUMBER OF INDEPENDENT NORMAL VARIATES
Anis, A. A., & Lloyd, E. H. (1953) · Biometrika · doi:10.1093/biomet/40.1-2.35 · Cited by 72
(iv) Proof of Relations connected with the Tetrachoric Series and its Generalization
Kendall, M. G. (1941) · Biometrika · doi:10.1093/biomet/32.2.196 · Cited by 67
Cited by
Multistage detection in asynchronous code-division multiple-access communications
Varanasi, M. K., & Aazhang, B. (1990) · IEEE Transactions on Communications · doi:10.1109/26.52662 · Cited by 1,259
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
Criminisi, A., Shotton, J., & Konukoglu, E. (2012) · Foundations and Trends® in Computer Graphics and Vision · doi:10.1561/0600000035 · Cited by 677
Tables for Computing Bivariate Normal Probabilities
Owen, D. B. (1956) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177728074 · Cited by 463
Entropy search for information-efficient global optimization
Hennig, P., & Schuler, C. J. (2012) · Journal of Machine Learning Research · doi:10.5555/2188385.2343701 · Cited by 443
Metadata
- Authors
- PLACKETT, R. L.
- Affiliations
- University of Liverpool (GB)
- Corresponding author
- PLACKETT, R. L.
- Venue
- Biometrika
- Publisher
- Oxford University Press (OUP)
- Published
- 1954
- Volume
- 41
- Issue
- 3-4
- Pages
- 351-360
- ISSN
- 0006-3444 (ISSN-L)
- 1464-3510
- OpenAlex
- W2029414932
- Semantic Scholar
- 532421d78ad43d301fbf63eea70a3af4f6fa116a
- Cited by
- 273
- References
- 8
- Citations by year
- 2026: 20 · 2025: 8 · 2024: 3 · 2023: 2 · 2022: 3 · 2021: 3 · 2020: 3 · 2019: 6 · 2018: 6 · 2017: 6 · 2016: 13 · 2015: 6 · 2014: 6 · 2013: 15 · 2012: 8
- FWCI
- 5.25
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Biometrika (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Applied Mathematics › Mathematical functions and polynomials
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Keywords
- reduction formulas, multivariate normal distribution
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- CoChat. (2026). Citation check: A REDUCTION FORMULA FOR NORMAL MULTIVARIATE INTEGRALS. https://app.cochat.ai/papers/10.1093/biomet/41.3-4.351
- The paper
- PLACKETT, R. L. (1954). A REDUCTION FORMULA FOR NORMAL MULTIVARIATE INTEGRALS. Biometrika. https://doi.org/10.1093/biomet/41.3-4.351
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
