The DOI matches its Crossref record; 1 of the 1 references it cites were found in a registry or an index.
Computation of Multivariate Normal and t Probabilities
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Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“Extensive comparisons amongst the numerous proposals in the literature (Genz and Bretz, 2009;Gassmann et al., 2002;Genz and Bretz, 2002) indicate the method of Genz (1992) is the most accurate across a wide range of test problems of medium and large dimensions.”
From The Normal Law Under Linear Restrictions: Simulation and Estimation via Minimax Tilting (2017) · cites this paper as Genz and Bretz, 2009
In the citing paper
“The first step in the Genz-Bretz algorithm is to compute a pivoted Cholesky factorization of the covariance matrix.”
From Doubly blocked variant of Genz’s method for multivariate normal integration (2026) · cites this paper as Genz and Bretz (2009)
In the citing paper
“It standardizes the bounds a and b by the square roots of the diagonal entries of Σ, divides each matrix entry Σ ij by √ Σ i,i Σ j,j , and chooses pivots so as to minimize the subsequent truncation or conditional variance.”
From Doubly blocked variant of Genz’s method for multivariate normal integration (2026) · cites this paper as Genz and Bretz (2009)
In the citing paper
“For tight bounds, reordering is crucial; adaptive reorder rules that update after a pilot run often halve variance in practice close to the optimal reordering (Genz and Bretz 2009).”
From Doubly blocked variant of Genz’s method for multivariate normal integration (2026) · cites this paper as Genz and Bretz 2009
In the citing paper
“It standardizes the bounds a and b by the square roots of the diagonal entries of Σ, divides each matrix entry Σ ij by √ Σ i,i Σ j,j , and chooses pivots so as to minimize the subsequent truncation or conditional variance.”
From Doubly blocked variant of Genz’s method for multivariate normal integration (2026) · cites this paper as Genz and Bretz (2009)
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Citations
Cites
Niederreiter, H., & Winterhof, A. (2015) · Springer eBooks · doi:10.1007/978-3-319-22321-6_4 · Cited by 48
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Rocher, L., Hendrickx, J. M., & de Montjoye, Y.-A. (2019) · Nature Communications · doi:10.1038/s41467-019-10933-3 · Cited by 816
Firth's logistic regression with rare events: accurate effect estimates and predictions?
Puhr, R., Heinze, G., Nold, M., Lusa, L., & Geroldinger, A. (2017) · Statistics in Medicine · doi:10.1002/sim.7273 · Cited by 483
Konietschke, F., Placzek, M., Schaarschmidt, F., & Hothorn, L. A. (2015) · Journal of Statistical Software · doi:10.18637/jss.v064.i09 · Cited by 315
Fahlgren, N., Feldman, M., Gehan, M. A., Wilson, M. S., Shyu, C., Bryant, D. W., Hill, S. T., McEntee, C. J., Warnasooriya, S. N., Kumar, I., et al. (2015) · Molecular Plant · doi:10.1016/j.molp.2015.06.005 · Cited by 281
Closed-skew normality in stochastic frontiers with individual effects and long/short-run efficiency
Colombi, R., Kumbhakar, S. C., Martini, G., & Vittadini, G. (2014) · Journal of Productivity Analysis · doi:10.1007/s11123-014-0386-y · Cited by 279
Metadata
- Authors
- Genz, A., & Bretz, F.
- Affiliations
- Medizinische Hochschule Hannover (DE)
- ORCID
- Bretz, Frank
- Venue
- Lecture Notes in Statistics
- Publisher
- Springer Berlin Heidelberg
- Published
- 2009
- ISSN
- 0930-0325 (ISSN-L)
- OpenAlex
- W1891298814
- Cited by
- 902
- References
- 1
- Citations by year
- 2026: 58 · 2025: 55 · 2024: 56 · 2023: 50 · 2022: 49 · 2021: 61 · 2020: 59 · 2019: 72 · 2018: 63 · 2017: 74 · 2016: 55 · 2015: 54 · 2014: 58 · 2013: 51 · 2012: 34
- FWCI
- 4.42
- Type
- book
- Language
- en
- Open access
- closed
- Licence
- www.springernature.com/gp/researchers/text-and-data-mining (tdm)
- www.springernature.com/gp/researchers/text-and-data-mining (vor)
- Locations
- Lecture notes in statistics (publishedVersion)
- International Linear Collider (submittedVersion)
- DIAL (Catholic University of Leuven) (submittedVersion)
- 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 › Statistics and Probability › Statistical Methods and Applications
- Keywords
- multivariate normal distribution, t-distribution, probability calculation, statistical inference, numerical integration
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Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Computation of Multivariate Normal and t Probabilities. https://app.cochat.ai/papers/10.1007/978-3-642-01689-9
- The paper
- Genz, A., & Bretz, F. (2009). Computation of Multivariate Normal and t Probabilities. Lecture Notes in Statistics. https://doi.org/10.1007/978-3-642-01689-9
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.
