Bootstrap Methods for Estimating the Confidence Interval for the Parameter of Zero-Truncated Poisson-Garima Distribution and Their Application

The zero-truncated count data are of primary interest in several areas such as biological science, medical science, demography, ecology, etc. Recently, the zero-truncated Poisson-Garima distribution has been proposed for such data. However, the confidence interval of its parameter has not yet been examined. In this paper, confidence interval estimation based on percentile, simple, biased-corrected and accelerated bootstrap methods, as well as the bootstrap-t interval, 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 methods were not substantially different. Overall, it is observed that the bias-corrected and accelerated bootstrap methods outperformed the others, even for small sample sizes. Lastly, the bootstrap methods were used to calculate the confidence interval for the zero-truncated Poisson-Garima parameter via two numerical examples, the results of which match those from the simulation study.