The Accuracy of a Modified Peizer Approximation to the Hypergeometric Distribution, with Comparisons to some Other Approximations

摘要

Results of an extensive empirical study of the accuracy of seven normal and three binomial approximations to the hypergeometric distribution are presented in terms of maximum absolute error under various conditions on the variables. The most useful condition is provided by the minimum cell in the given or complementary 2 2 table and the tail probability itself. Of the normal approximations, a modification on one due to Peizer is far the best. It has error at most .0001, for example, if the minimum cell is at least 9, or if the tail probability is below .01 and the minimum cell is at least 4. Especially detailed results are given for this approximation.