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Growth Estimators and Confidence Intervals for the Mean of Negative Binomial Random Variables with Unknown Dispersion
Joint Authors
Source
Journal of Probability and Statistics
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-08-26
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
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 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, predetermined 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.
American Psychological Association (APA)
Shilane, David& Bean, Derek. 2013. Growth Estimators and Confidence Intervals for the Mean of Negative Binomial Random Variables with Unknown Dispersion. Journal of Probability and Statistics،Vol. 2013, no. 2013, pp.1-9.
https://search.emarefa.net/detail/BIM-484238
Modern Language Association (MLA)
Shilane, David& Bean, Derek. Growth Estimators and Confidence Intervals for the Mean of Negative Binomial Random Variables with Unknown Dispersion. Journal of Probability and Statistics No. 2013 (2013), pp.1-9.
https://search.emarefa.net/detail/BIM-484238
American Medical Association (AMA)
Shilane, David& Bean, Derek. Growth Estimators and Confidence Intervals for the Mean of Negative Binomial Random Variables with Unknown Dispersion. Journal of Probability and Statistics. 2013. Vol. 2013, no. 2013, pp.1-9.
https://search.emarefa.net/detail/BIM-484238
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-484238