2013
DOI: 10.1155/2013/602940
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Growth Estimators and Confidence Intervals for the Mean of Negative Binomial Random Variables with Unknown Dispersion

Abstract: 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 expected value 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 Bernste… Show more

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“…Shilane et al (2010) established that the normal confidence interval significantly under-covers the mean at moderate sample sizes and suggested alternative estimators based upon gamma and chi square approximations along with tail probability bounds such as Bernstein's inequality. Shilane and Bean (2013) proposed another method, namely the growth estimator, which provides improved confidence intervals for the mean of negative binomial random variables with unknown dispersion. They observed that their growth estimator produces intervals that are longer and more variable than the normal approximation.…”
Section: Introductionmentioning
confidence: 99%
“…Shilane et al (2010) established that the normal confidence interval significantly under-covers the mean at moderate sample sizes and suggested alternative estimators based upon gamma and chi square approximations along with tail probability bounds such as Bernstein's inequality. Shilane and Bean (2013) proposed another method, namely the growth estimator, which provides improved confidence intervals for the mean of negative binomial random variables with unknown dispersion. They observed that their growth estimator produces intervals that are longer and more variable than the normal approximation.…”
Section: Introductionmentioning
confidence: 99%