### Abstract

It is shown that a km-variate normal probability integral over a rectangular region can be expressed as an iterated k-variate normal integral when the k sets of m variates each have a certain commonly realized block covariance structure. The latter representation is much easier to evaluate numerically than is the former. This result generalizes previous results for k= 1 of Dunnett & Sobel and Steck & Owen.

Original language | English (US) |
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Pages (from-to) | 615-619 |

Number of pages | 5 |

Journal | Biometrika |

Volume | 61 |

Issue number | 3 |

DOIs | |

State | Published - Dec 1 1974 |

### Keywords

- Block covariance strucutre
- Multivariate normal integral
- Multivariate normal probabilities
- Numerical integration
- Ranking and selection procedures

### ASJC Scopus subject areas

- Statistics, Probability and Uncertainty
- Applied Mathematics
- Mathematics(all)
- Statistics and Probability
- Agricultural and Biological Sciences (miscellaneous)
- Agricultural and Biological Sciences(all)

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## Cite this

Bechhofer, R. E., & Tamhane, A. C. (1974). An iterated integral representation for a multivariate normal integral having block covariance structure.

*Biometrika*,*61*(3), 615-619. https://doi.org/10.1093/biomet/61.3.615