Premium
Saddlepoint approximations to the mean and variance of the extended hypergeometric distribution
Author(s) -
Eisinga Rob,
Pelzer Ben
Publication year - 2011
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.2010.00468.x
Subject(s) - hypergeometric distribution , mathematics , variance (accounting) , approximations of π , hypergeometric function , distribution (mathematics) , conditional probability distribution , statistics , mathematical analysis , accounting , business
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.