Non-parametric bootstrap confidence intervals for index of dispersion of zero-truncated Poisson-Lindley distribution

The Poisson distribution may not fit the data in several real-life circumstances. In this case the zero-truncated Poisson-Lindley (ZTPL) distribution has been proposed as a statistical model for counting data that do not include zero values. The index of dispersion (IOD) is a valuable tool for evaluating the suitability of the distribution in modelling observed count data. Nevertheless, the examination of the non-parametric bootstrap method for estimating confidence intervals (CIs) of the IOD of the ZTPL distribution has not been conducted. The study of the non-parametric bootstrap CI for the IOD can provide a more nuanced and informative understanding of data variability. This is crucial for various applications including comparisons between groups, risk assessment, decision-making, and ensuring the robustness of statistical conclusions. This study aims to investigate the performance of non-parametric bootstrap CIs derived from percentile, simple, and bias-corrected bootstrapping methods. Coverage probability and average length are evaluated using Monte Carlo simulation. The simulation results demonstrate that achieving the designated confidence level using non-parametric bootstrap CIs is unattainable for small sample sizes, irrespective of the other parameters. In addition, the performance of the non-parametric bootstrap CIs does not differ significantly when the sample size is large. The bias-corrected bootstrap CI demonstrates superior performance compared to other methods, even when dealing with limited sample sizes. Using two numerical examples, non-parametric bootstrap methods are utilised to calculate the CI for the IOD of a ZTPL distribution. The results match those of the simulation study.