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- Title
Non-parametric bootstrap confidence intervals for index of dispersion of zero-truncated Poisson-Lindley distribution.
- Authors
Panichkitkosolkul, Wararit
- Abstract
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 biascorrected 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 nonparametric bootstrap CIs does not differ significantly when the sample size is large. The biascorrected 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.
- Subjects
MONTE Carlo method; CONFIDENCE intervals; STATISTICAL decision making; POISSON distribution; STATISTICAL models; DISPERSION (Chemistry)
- Publication
Maejo International Journal of Science & Technology, 2024, Vol 18, Issue 1, p1
- ISSN
1905-7873
- Publication type
Article