Bootstrap Methods for Estimating the Confidence Interval for the Parameter of Zero-Truncated Poisson-Garima Distribution and Their Application
Author affiliations
DOI:
https://doi.org/10.15625/2525-2518/18056Abstract
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.
Downloads
References
1. Kissell R., Poserina J. - Optimal sports math, statistics, and fantasy, Academic Press, London, 2017.
2. Andrew F. S., Michael R. W. - Practical business statistics, Academic Press, London, 2022.
3. Montgomery D. C., Runger G. C. - Applied statistics and probability for engineers, John Wiley & Sons, Noida, 2003.
4. Sangnawakij P. - Confidence interval for the parameter of the zero-truncated Poisson distribution, J. Appl. Sci. 20 (2021) 13-22.
5. Hougaard P., Lee M. L. T., Whitmore G. A. - Analysis of overdispersed count data by mixtures of Poisson variables and Poisson processes, Biometrics 53 (1997) 1225-1238.
6. McElduff F. C. - Models for discrete epidemiological and clinical data, Ph.D. dissertation, University College London, 2012.
7. Ong S. H., Low Y. C., Toh K. K. - Recent developments in mixed Poisson distributions, ASM Sci. J. (2021) https://doi.org/10.32802/asmscj.2020.464.
8. Tharshan R., Wijekoon P. - A new mixed Poisson distribution for over-dispersed count data: Theory and applications, Reliab.: Theory Appl. 17 (2022) 33-51.
9. Shanker R. - The discrete Poisson-Garima distribution, Biom. Biostat. Int. J. 5 (2017) 1-7.
10. Shanker R. - Garima distribution and its application to model behavioral science data, Biom. Biostat. Int. 4 (2016) 1-9.
11. Sankaran M. - The discrete Poisson-Lindley distribution, Biometrics 26 (1970) 145-149.
12. Lindley D. V. - Fiducial distributions and Bayes’ theorem, J. R. Stat. Soc. B. 20 (1958) 102-107.
13. Shanker R. - Akash distribution and its applications, Int. J. Stat. Appl. 4 (2015b) 65-75.
14. Shanker R. - Aradhana distribution and its applications, Int. J. Stat. Appl. 6 (2016a) 23-34.
15. Shanker R. - Sujatha distribution and its applications, Stat. Transit. 17 (2016c) 1-20.
16. David F., Johnson N. - The truncated Poisson, Biometrics 8 (1952) 275-285.
17. Hussain T. - A zero truncated discrete distribution: Theory and applications to count data, Pak. J. Stat. Oper. Res. 16 (2020) 167-190.
18. Ghitany M. E., Al-Mutairi D. K., Nadarajah S. - Zero-truncated Poisson-Lindley distribution and its application, Math. Comput. Simul. 79 (2008) 279-287.
19. Shanker R., Hagos F. - Zero-truncated Poisson-Sujatha distribution with applications, J. Ethiopian Stat. Assoc. 24 (2015) 55-63.
20. Shanker R. - Zero-truncated Poisson-Akash distribution and its applications, Am. J. Math. Stat. 7 (2017) 227-236.
21. Shanker R., Shukla K. K. - Zero-truncated Poisson-Garima distribution and its applications, Biostat. Biom. 3 (2017) 1-6.
22. Tan S. H., Tan S. B. - The correct interpretation of confidence intervals, Proceedings of Singapore Healthcare 19 (2010) 276-278.
23. Wood M. - Statistical inference using bootstrap confidence intervals, Signif. 1 (2004) 180-182.
24. Chernick M. R., LaBudde R. A. - An introduction to bootstrap methods to R, John Wiley & Sons, New York, 2014.
25. Henningsen A., Toomet O. - maxLik: A package for maximum likelihood estimation in R, Comput. Stat. 26 (2011) 443-458.
26. Ihaka R., Gentleman R. - R: A language for data analysis and graphics, J. Comput. Graph. Stat. 5 (1996) 299-314.
27. Flowers-Cano R. S., Ortiz-Gómez R., León-Jiménez J. E., López Rivera R., Perera Cruz L. A. - Comparison of bootstrap confidence intervals using Monte Carlo simulations, Water 10 (2018) 166, https://doi.org/10.3390/w.10020166.
28. Van den Boogaard H. F. P., Hall M. J. - The construction of confidence intervals for frequency analysis using resampling techniques: A supplementary note, Hydrol. Earth Syst. Sci. 8 (2004) 1174-1178.
29. Meeker W. Q., Hahn G. J., Escobar L. A. - Statistical intervals: A guide for practitioners and researchers, John Wiley and Sons, New York, 2017.
30. Efron B. - The Jackknife, the bootstrap, and other resampling plans, in CBMS-NSF Regional Conference Series in Applied Mathematics, Monograph 38, SIAM, Philadelphia, 1982.
31. Efron B., Tibshirani R. J. - An introduction to the bootstrap, Chapman and Hall, New York, 1993.
32. Efron B. - Better bootstrap confidence intervals, J. Am. Stat. Assoc. 82 (1987) 171-185.
33. Shanker R. Fesshaye H., Selvaraj S., Yemane A. - On zero-truncation of Poisson and Poisson-Lindley distributions and their applications, Biom. Biostat. Int. J. 2 (2015) 168-181.
34. Turhan N. S. - Karl Pearson’s chi-square tests, Educ. Res. Rev. 15 (2020) 575-580.
35. Garman P. - The European red mites in Connecticut apple orchards, Connecticut. Agri. Exper. Station. Bull. 252 (1923) 103-125.
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Vietnam Journal of Sciences and Technology (VJST) is an open access and peer-reviewed journal. All academic publications could be made free to read and downloaded for everyone. In addition, articles are published under term of the Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA) Licence which permits use, distribution and reproduction in any medium, provided the original work is properly cited & ShareAlike terms followed.
Copyright on any research article published in VJST is retained by the respective author(s), without restrictions. Authors grant VAST Journals System a license to publish the article and identify itself as the original publisher. Upon author(s) by giving permission to VJST either via VJST journal portal or other channel to publish their research work in VJST agrees to all the terms and conditions of https://creativecommons.org/licenses/by-sa/4.0/ License and terms & condition set by VJST.
Authors have the responsibility of to secure all necessary copyright permissions for the use of 3rd-party materials in their manuscript.
Vietnam Journal of Science and Technology (VJST) is pleased to notice: