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An Approximation to Certain Multivariate Normal Probabilities
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DOI：10.1111/j.2517-6161.1981.tb01152.x.png)
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Abstract
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Summary
In models of disease transmission, in which liability to disease is assumed to be normally distributed, the problem arises of calculating the probability that a given member of a group of individuals will contract the disease conditional on the other members exceeding some threshold. 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.
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