Small Sample Comparison of Different Estimators of Negative Binomial Parameters

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Abstract
Four methods of estimating the negative binomial parameters from small samples were examined: moment, maximum likelihood (ML), digamma and zero-class estimators. The latter 2 estimators have no redeeming features as compared to the former 2 methods and have substantial characteristics. The moment and ML estimators for parameter K appear to exhibit similar characteristics. The moment estimator for parameter p appears to be inferior to the ML estimators with respect to frequency and magnitude of bias. It is recommended for small sample size calculating the moment estimators for p and k; the ML estimators need be calculated only if p .gtoreq. k. The parameters of the negative binomial distribution were fitted by the moment and ML estimators using extensive arthropod data collected on cotton plants. Tests for homogeneity of k were made using Bliss and Owen''s technique; the common k thus calculated was nearly always less than the average of the ML estimators.

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