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Biometrika 1979 66(3):585-590; doi:10.1093/biomet/66.3.585
© 1979 by Biometrika Trust
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Testing the goodness of fit of the binomial distribution

R. E. TARONE

National Cancer Institute Bethesda, Maryland

Using the C({alpha}) procedure of Neyman (1959), we derive teats for the goodness of fit of the binomial distribution which are asymptotically optimal against generalized binomial alternatives proposed by Altham (1978) and Kupper & Haseman (1978). The C({alpha}) tests optimal against correlated binomial alternatives, beta-binomial alternatives and a general class of mixture alternatives suggested by WisniewsM (1968) are shown to be closely related to the binomial variance test. A numerical example is given and the small sample behaviour of the variance test and the C({alpha}) tests is investigated in a Monte Carlo sampling experiment. The asymptotic relative efficiencies of the goodness of fit statistics are examined.

Key Words: Asymptotic relative efficiency • Beta-binomial • C({alpha}) tests • Generalized binomial distributions • Goodness of fit • Pitman efficiency


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