Small Sample Comparison of Different Estimators of Negative Binomial Parameters

Four methods of estimating the negative binomial parameters from small samples were examined: moment, maximum likelihood (ML), digamma and zero-class estimators. The latter two estimators have no redeeming features as compared to the former two methods and have substantial disadvantages. The moment and ML estimators for parameter k appear to exhibit similar characteristics. However, the moment estimator for parameter p appears to be inferior to the ML estimators with respect to frequency and magnitude of bias. We recommend for small sample size calculating the moment estimators for p and k; the ML estimators need be calculated only if p $\geq$ k. The parameters of the negative binomial distribution were fitted by the moment and ML estimators using extensive arthropod data collected on cotton plants. In addition 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.