Confidence Intervals using Bootstrap Methods for the Parameter of the zero-truncated Poisson-Shanker Distribution and their Application

Abstract

Several situations involve count data containing non-zero values and the zero-truncated Poisson-Shanker distribution can be used to model such data. However, the confidence interval estimation of the parameter has not yet been examined. In this paper, confidence interval estimation based on percentile bootstrap, simple bootstrap, biased-corrected and accelerated bootstrap, and bootstrap-t 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 were 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, the bias-corrected and accelerated bootstrap method outperformed the others, even for small sample sizes. Last, the bootstrap methods were used to calculate the confidence interval for the parameter of the zero-truncated Poisson-Shanker distribution via three numerical examples, the results of which match those from the simulation study.