Bootstrap Confidence Intervals for the Index of Dispersion of Zero-Truncated Poisson-Ishita Distribution

Abstract

The zero-truncated Poisson-Ishita distribution has been proposed for the count data without zero values, such as the number of items in a shopper’s basket at a supermarket checkout line and the length of stay in hospital. However, the confidence interval estimation of the index of dispersion has not yet been examined. In this paper, confidence interval estimation based on percentile, simple, and biased-corrected and accelerated bootstrap methods was examined in terms of coverage probability and average length via Monte Carlo simulation. The results indicate that attaining the nominal confidence level using the bootstrap methods was not possible for small sample sizes regardless of the other settings. Moreover, when the sample size was large, the performances of the bootstrap methods were not substantially different. Overall, the simple bootstrap method outperformed the others, even for medium and large sample sizes. Lastly, the bootstrap methods were used to calculate the confidence interval for the index of dispersion of the zero truncated Poisson-Ishita distribution via two numerical examples, the results of which match those from the simulation study.