Nonparametric Bootstrap Confidence Intervals for the Population Mean of a Zero-Truncated Poisson-Lindley Distribution and Their Application

Recently, the zero-truncated Poisson-Lindley distribution has been proposed for studying count data containing non-zero values. However, the nonparametric bootstrap confidence interval estimation of the population mean has not yet been studied. In this study, confidence interval estimation based on percentile, simple, and biased-corrected bootstrap methods was compared in terms of coverage probability and average interval length via Monte Carlo simulation. The true values of parameter ()  were set as 0.25, 0.5, 1, 1.5, and 2, and the population means  are approximate 7.7586, 4.0909, 2.4000, 1.8817, and 1.6364, respectively. The bootstrap samples (=1,000)  of size  were generated from the original sample, and each simulation was repeated 1,000 times. The results indicate that attaining the nominal confidence level using the bootstrap confidence intervals was impossible for small sample sizes regardless of the other settings. Moreover, when the sample size was large, the performance of the nonparametric bootstrap confidence intervals was not substantially different. Overall, the bias-corrected bootstrap confidence interval outperformed the others, even for small sample sizes. Last, the nonparametric bootstrap confidence intervals were used to calculate the confidence interval for the population mean of the zero-truncated Poisson-Lindley distribution via two numerical examples, the results of which match those from the simulation study.