The DOI matches its Crossref record; 10 of the 10 references it cites were found in a registry or an index.
The numerical evaluation of a class of integrals. II
Abstract
Consider the integral where x1, x2, …, x N are jointly distributed in a multivariate normal distribution f(x1, x2, …, x N) with (p ij) as the correlation matrix. The integral has been expressed in an infinite series of tetrachoric functions for N≥2. The infinite series is not only complicated, but also is very slowly convergent and is consequently not of much practical use. Plackett (8) obtains a reduction formula for expressing normal integrals in four variates as a finite sum of single integrals of tabulated functions. These integrals have then to be evaluated by a rather awkward numerical quadrature.
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Cites
A REDUCTION FORMULA FOR NORMAL MULTIVARIATE INTEGRALS
PLACKETT, R. L. (1954) · Biometrika · doi:10.1093/biomet/41.3-4.351 · Cited by 273
A reduction formula for normal multivariate integrals
Plackett, R. L. (1954) · Biometrika · doi:10.2307/2332716 · Cited by 262
The evaluation of integrals of the form
Goodwin, E. T. (1949) · Mathematical Proceedings of the Cambridge Philosophical Society · doi:10.1017/s0305004100024786 · Cited by 117
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
(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
The Theory of Infinite Series.
Ramanujan, M. S., Bhatnagar, P. L., & Srinivasiengar, C. N. (1966) · American Mathematical Monthly · doi:10.2307/2315451 · Cited by 54
The numerical evaluation of a class of integrals
Moran, P. A. P. (1956) · Mathematical Proceedings of the Cambridge Philosophical Society · doi:10.1017/s0305004100031212 · Cited by 34
On the Shape of the Angular Case of Cauchy's Distribution Curves
Wintner, A. (1947) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177730351 · Cited by 26
A SUMMATION FORMULA ASSOCIATED WITH FINITE TRIGONOMETRIC INTEGRALS
Kendall, D. G. (1942) · The Quarterly Journal of Mathematics · doi:10.1093/qmath/os-13.1.172 · Cited by 10
Research works printed but not linked: 1
- Kendall, 1941, Biometrika, 32, 196
Cited by
A Table for Computing Trivariate Normal Probabilities
Steck, G. P. (1958) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177706536 · Cited by 77
On Selecting the Largest of k Normal Population Means
Dunnett, C. W. (1960) · Journal of the Royal Statistical Society Series B (Statistical Methodology) · doi:10.1111/j.2517-6161.1960.tb00351.x · Cited by 63
Orthant Probabilities for the Equicorrelated Multivariate Normal Distribution
Steck, G. P. (1962) · Biometrika · doi:10.1093/biomet/49.3-4.433 · Cited by 36
On higher-dimensional analogues of the arc-sine law
Bingham, Ν. H., & Doney, R. A. (1988) · Journal of Applied Probability · doi:10.1017/s0021900200040699 · Cited by 35
Pettitt, A. N. (1986) · Biometrika · doi:10.1093/biomet/73.3.635 · Cited by 34
Metadata
- Authors
- Das, S. C.
- Affiliations
- Australian National University (AU)
- Corresponding author
- Das, S. C.
- ORCID
- Das, S. C.
- Venue
- Mathematical Proceedings of the Cambridge Philosophical Society
- Publisher
- Cambridge University Press (CUP)
- Published
- 1956-07
- Volume
- 52
- Issue
- 3
- Pages
- 442-448
- ISSN
- 0305-0041 (ISSN-L)
- 1469-8064
- OpenAlex
- W2098010348
- Semantic Scholar
- 50c0950862f938c0a50108e90cb115d1ffb91b59
- Cited by
- 18
- References
- 9
- FWCI
- 1.64
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Mathematical Proceedings of the Cambridge Philosophical Society (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Applied Mathematics › Mathematical functions and polynomials
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
- Physical Sciences › Mathematics › Numerical Analysis › Mathematical Approximation and Integration
- Keywords
- multivariate normal distribution, numerical evaluation of integrals, infinite series, reduction formulas, numerical quadrature, correlation matrix
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- The paper
- Das, S. C. (1956). The numerical evaluation of a class of integrals. II. Mathematical Proceedings of the Cambridge Philosophical Society. https://doi.org/10.1017/s0305004100031443
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