Bootstrap Methods for Estimating the Confidence Interval for the Index of Dispersion of the Zero-Truncated Poisson-Amarendra Distribution

Abstract

The zero-truncated count data is of primary interest in many areas such as biological science, medical science, demography, ecology, etc. Recently, the zero-truncated Poisson-Amarendra distribution has been proposed for such data. 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, biased-corrected and accelerated bootstrap methods was examined in terms of coverage probability and average interval 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 methods were not substantially different. However, the percentile bootstrap and the simple bootstrap methods provided the shortest average lengths for small sample sizes. Last, the bootstrap methods were used to calculate the confidence intervals for the index of dispersion of the zero-truncated Poisson-Amarendra distribution via two numerical examples, the results of which match those from the simulation study.