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The Negative Binomial distribution becomes highly skewed under extremedispersion. Even at moderately large sample sizes, the sample mean exhibits aheavy right tail. The standard Normal approximation often does not provideadequate inferences about the data's mean in this setting. In previous work, wehave examined alternative methods of generating confidence intervals for theexpected value. These methods were based upon Gamma and Chi Squareapproximations or tail probability bounds such as Bernstein's Inequality. Wenow propose growth estimators of the Negative Binomial mean. Under highdispersion, zero values are likely to be overrepresented in the data. A growthestimator constructs a Normal-style confidence interval by effectively removinga small, pre--determined number of zeros from the data. We propose growthestimators based upon multiplicative adjustments of the sample mean and directremoval of zeros from the sample. These methods do not require estimating thenuisance dispersion parameter. We will demonstrate that the growth estimators'confidence intervals provide improved coverage over a wide range of parametervalues and asymptotically converge to the sample mean. Interestingly, theproposed methods succeed despite adding both bias and variance to the Normalapproximation.

Growth Estimators and Confidence Intervals for the Mean of Negative Binomial Random Variables with Unknown Dispersion