Abstract
A simple estimator, p = n/(n + X + l), for the negative binomial parameter p is derived to satisfy approximately E. J. G. Pitman's definition of “closeness.” The mean, variance, and mean-squared error of p are investigated analytically using a technique (an extension of work by D. J. Finney) for expanding an arbitrary function of a negative-binomially disributed random variable in an infinite series. Extensive numerical computations indicate that for a wide range of useful values of n and p, p is “closer” and has smaller mean-squared error than some other well-known estimators for p. Such an estimator should be particularly useful in applications of inverse binomial sampling, where negative binomial distributions involving small values of n and p are encountered.
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