Estimation of the shape parameter k of the negative binomial distribution

Using approximate Bayesian methods, an estimator of the shape parameter of the negative binomial distribution is introduced. Most of the available estimators of this parameter, such as the method of moment and the maximum likelihood estimators (MME and MLE), give inadmissible values when the mean of the observed sample is larger than its variance. In this case, the MME gives values while the MLE is infinite. Such observed sample in not unlikely when the mean of the population is close to its variance. The suggested estimator always has valid values, and turned out to be more efficient for most values of the parameter space. Family size data is used for illustration of the procedure.

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