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Biometrika 1986 73(2):425-435; doi:10.1093/biomet/73.2.425
© 1986 by Biometrika Trust
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The bias and higher cumulants of the logarithm of a binomial variate

HUGH M. PETTIGREW, JOHN J. GART and DONALD G. THOMAS

Mathematical Statistics and Applied Mathematics Section, Biostatistics Branch, National Cancer Institute Bethesda, Maryland 20892, U.S.A.

The bias and first four cumulants of the distribution of the logarithm of a binomial variate are studied by means of asymptotic expansions and exact computation. A new estimator of the variance is derived and evaluated. The asymptotic skewness is found to differ from the result of Walter (1975). Applications to point estimation of the one-hit curve and the interval estimation and testing of the ratio of binomial parameters are considered. Because of the bias and nonnormality of such statistics, methods based on likelihood methods or Pearson chi-squared statistics are preferred.

Key Words: Attributable risk • Bias • Binomial distribution • Kurtosis • Log transformation • One-hit curve • Relative risk • Skewness


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