The Accuracy of Peizer Approximations to the Hypergeometric Distribution, with Comparisons to Some other Approximations

Abstract

Results of an extensive empirical study of the accuracy of 12 normal and 3 binomial approximations to the hypergeometric distribution are presented in terms of maximum absolute error under various conditions on the variables. The most useful conditions employ the minimum cell in the given or complementary 2 × 2 table and the tail probability itself. Of the normal approximations, the best by far are of a heretofore unpublished type originated by Peizer. Especially detailed results on both absolute and relative errors are given for one Peizer approximation. Its absolute error is at most .0001, for example, if the minimum cell is at least 4.

Key Words:

• Maximum absolute error
• Hypergeometric distribution
• Normal approximation
• Binomial approximation
• Relative error