Saddlepoint approximations to the mean and variance of the extended hypergeometric distribution |
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Authors: | Rob Eisinga Ben Pelzer |
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Institution: | Department of Social Science Research Methods, Radboud University Nijmegen, PO Box 9104, 6500 HE Nijmegen, The Netherlands |
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Abstract: | Conditional inference on 2 x 2 tables with fixed margins and unequal probabilities is based on the extended hypergeometric distribution. If the support of the distribution is large, exact calculation of the conditional mean and variance of the table entry may be computationally demanding. This paper proposes a single‐saddlepoint approximation to the mean and variance. While the approximation achieves acceptable accuracy for ordinary practical purposes, an alternative saddlepoint approximation is provided that gives much closer to exact results. It improves the accuracy of current approximations to up to more than four powers of ten. |
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Keywords: | extended hypergeometric distribution saddlepoint approximation 2 x 2 table |
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