A Comparison of Several Methods for the Confidence Intervals of Negative Binomial Proportions

摘要

This study focuses on the comparison of the performances of several approaches in constructing confidence interval of negative binomial proportions (single negative binomial proportion and the difference between two negative binomial proportions). After that, the strengths and weaknesses of the approaches in constructing confidence interval of negative binomial proportions are figured out. Performances of the approaches will be accessed by comparing their coverage probabilities and average lengths of confidence intervals. For the comparison of the performances of the approaches in single negative binomial proportion, Wald confidence interval (WCI-I), Agresti confidence interval (ACI-I), Wilson's Score confidence interval (WSCI-I) and Jeffrey confidence interval (JCI-I) are used. WSCI-I is the better approach for single negative binomial proportion in term of the average length of confidence intervals and average coverage probability. While for the comparison of the performances of the approaches in the difference between two negative binomial proportions, Wald confidence interval (WCI-II), Agresti confidence interval (ACI-II), Newcombe's Score confidence interval (NSCI-II), Jeffrey confidence interval (JCI-II) and Yule confidence interval (YCI-II) are used. Under different situations, a better approach has been discussed and recommended. There will be different approach that performs better for the coverage probability.