The evaluation of general non-centred orthant probabilities
成果类型：
Article
署名作者：
Miwa, T; Hayter, AJ; Kuriki, S
署名单位：
National Institute for Agro-Environmental Sciences (NIAES) Japan; University System of Georgia; Georgia Institute of Technology; Research Organization of Information & Systems (ROIS); Institute of Statistical Mathematics (ISM) - Japan
刊物名称：
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
ISSN/ISSBN：
1369-7412
DOI：
10.1111/1467-9868.00382
发表日期：
2003
页码：
223-234
关键词：
摘要：
The evaluation of the cumulative distribution function of a multivariate normal distribution is considered. The multivariate normal distribution can have any positive definite correlation matrix and any mean vector. The approach taken has two stages. In the first stage, it is shown how non-centred orthoscheme probabilities can be evaluated by using a recursive integration method. In the second stage, some ideas of Schlafli and Abrahamson are extended to show that any non-centred orthant probability can be expressed as differences between at most (m - 1)! non-centred orthoscheme probabilities. This approach allows an accurate evaluation of many multivariate normal probabilities which have important applications in statistical practice.
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