  The Negative Binomial distribution becomes highly skewed under extreme
dispersion. Even at moderately large sample sizes, the sample mean exhibits a
heavy right tail. The standard Normal approximation often does not provide
adequate inferences about the data's mean in this setting. In previous work, we
have examined alternative methods of generating confidence intervals for the
expected value. These methods were based upon Gamma and Chi Square
approximations or tail probability bounds such as Bernstein's Inequality. We
now propose growth estimators of the Negative Binomial mean. Under high
dispersion, zero values are likely to be overrepresented in the data. A growth
estimator constructs a Normal-style confidence interval by effectively removing
a small, pre--determined number of zeros from the data. We propose growth
estimators based upon multiplicative adjustments of the sample mean and direct
removal of zeros from the sample. These methods do not require estimating the
nuisance dispersion parameter. We will demonstrate that the growth estimators'
confidence intervals provide improved coverage over a wide range of parameter
values and asymptotically converge to the sample mean. Interestingly, the
proposed methods succeed despite adding both bias and variance to the Normal
approximation.
