Summary  Best [1] found the variance of the minimum variance unbiased estimator of the parameter p of the negative binomial distribution. Mikulski and Sm [2] gave an upper bound to it, easier to calculate than Best's expression and a good approximation for small values of p and large values of r (the number of successes). In this paper both lower bounds and closer upper bounds are derived. Copyright

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Journal Statistica Neerlandica
Sahai, A, & Buhrman, J.M. (1979). Bounds for the variance of an inverse binomial estimator. Statistica Neerlandica, 33(4), 213–215. doi:10.1111/j.1467-9574.1979.tb00676.x