Saddlepoint approximations to the mean and variance of the extended hyper geometric distribution

R. Eisinga, B. Pelzer

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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 givesmuch closer to exact results. It improves the accuracy of current approximations to up to more than four powers of ten.
Original languageEnglish
Pages (from-to)22-31
Number of pages10
JournalStatistica Neerlandica
Issue number1
Publication statusPublished - 2010


  • saddlepoint approximation
  • 2 x 2 table
  • extended hypergeometric distribution

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