Bootstrap Methods for Estimating the Confidence Interval for the Index of Dispersion of the Zero-truncated Poisson-Shanker Distribution
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Abstract
The zero-truncated Poisson-Shanker distribution (ZTPS) has been introduced for count data, which is of primary interest in several fields. However, the construction of bootstrap confidence intervals for its index of dispersion (IOD) has not yet been studied. The bootstrap confidence intervals using the percentile, simple, biased-corrected, and accelerated bootstrap methods were proposed in this paper. A Monte Carlo simulation study was conducted to evaluate the performance of three bootstrap confidence intervals based on the coverage probability and average length of the bootstrap confidence intervals. The results indicate that attaining the nominal confidence level using the bootstrap methods was impossible for small sample sizes regardless of the other settings.
Moreover, when the sample size was large, the performances of all methods were not substantially different. The percentile bootstrap and the simple bootstrap methods perform well regarding coverage probability and average length for large sample sizes. However, calculating the percentile bootstrap method is easier than calculating the simple bootstrap method. In the end, real data sets from different fields were analyzed to verify the usefulness of the bootstrap confidence intervals. It is manifested that the results match those from the simulation study.
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