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The special case in which the truncated variables are uncorrelated with each other occurs frequently and we consider here an approximation, based on a Gram-Charlier expansion, for the probabilities which arise in this case. In two dimensions the method is a serious rival to the tetrachoric series expansion only for large positive truncation levels. In higher dimensions other methods are either approximate or difficult to use.<\/jats:p>","DOI":"10.1111\/j.2517-6161.1981.tb01152.x","type":"journal-article","created":{"date-parts":[[2018,12,7]],"date-time":"2018-12-07T05:14:32Z","timestamp":1544159672000},"page":"81-85","source":"Crossref","is-referenced-by-count":8,"title":["An Approximation to Certain Multivariate Normal Probabilities"],"prefix":"10.1093","volume":"43","author":[{"given":"R. J.","family":"Henery","sequence":"first","affiliation":[{"name":"University of Strathclyde \u00a0 Scotland U.K."}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"286","published-online":{"date-parts":[[2018,12,5]]},"reference":[{"key":"2024090921065147100_rssb01152-cit-0001","volume-title":"Handbook of Mathematical Functions.","author":"Abramowitz","year":"1964"},{"key":"2024090921065147100_rssb01152-cit-0002","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2307\/1401275","article-title":"The consequences of selection for a variate subject to errors of measurement","volume":"24","author":"Finney","year":"1956","journal-title":"Rev. Inst. Int. Statist."},{"key":"2024090921065147100_rssb01152-cit-0003","volume-title":"Distributions in Statistics, Continuous Multivariate Distributions.","author":"Johnson","year":"1972"},{"key":"2024090921065147100_rssb01152-cit-0004","volume-title":"The use of the tetrachoric series for evaluating multivariate normal probabilities","author":"Harris","year":"1979"},{"key":"2024090921065147100_rssb01152-cit-0005","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1111\/j.1469-1809.1980.tb01561.x","article-title":"An easy method for calculating approximate recurrence risks using a multi-factorial model of disease transmission","volume":"43","author":"Hutchinson","year":"1979","journal-title":"Ann. 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Human Gen.,","author":"Hutchinson","year":"1980"},{"key":"2024090921065147100_rssb01152-cit-0007","volume-title":"The Advanced Theory of Statistics","author":"Kendall","year":"1969"},{"key":"2024090921065147100_rssb01152-cit-0008","doi-asserted-by":"crossref","first-page":"41","DOI":"10.2307\/2529616","article-title":"Multifactorial traits: genetic analysis and prediction of recurrence risks","volume":"30","author":"Mendell","year":"1974","journal-title":"Biometrics"},{"key":"2024090921065147100_rssb01152-cit-0009","doi-asserted-by":"crossref","first-page":"1075","DOI":"10.1214\/aoms\/1177728074","article-title":"Tables for computing the bivariate normal probabilities","volume":"27","author":"Owen","year":"1956","journal-title":"Ann. Math. 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B"}],"container-title":["Journal of the Royal Statistical Society Series B: Statistical Methodology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1111%2Fj.2517-6161.1981.tb01152.x","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/43\/1\/81\/49099441\/jrsssb_43_1_81.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jrsssb\/article-pdf\/43\/1\/81\/49099441\/jrsssb_43_1_81.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,9]],"date-time":"2024-09-09T22:04:14Z","timestamp":1725919454000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jrsssb\/article\/43\/1\/81\/7028093"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1981,9,1]]},"references-count":13,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2018,12,5]]},"published-print":{"date-parts":[[1981,9,1]]}},"URL":"https:\/\/doi.org\/10.1111\/j.2517-6161.1981.tb01152.x","relation":{},"ISSN":["1369-7412","1467-9868"],"issn-type":[{"value":"1369-7412","type":"print"},{"value":"1467-9868","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[1981,9]]},"published":{"date-parts":[[1981,9,1]]}}}