Analyzing meteorological data with bootstrap-based confidence intervals for Poisson-Rani distribution parameter estimation
Article Sidebar
Main Article Content
Abstract
The Poisson distribution is commonly used when events are assumed to be independent and occur at a consistent rate. This may not be generally applicable, and the Poisson distribution is not appropriate in situations where the underlying rate of occurrence displays variability. A mixed Poisson distribution such as the Poisson-Rani distribution permits the rate parameter to be random instead of constant. Bootstrap-based confidence intervals (CIs) were developed for the Poisson-Rani distribution parameter in this study. The percentile bootstrap (PB), basic bootstrap (BB), and bias-corrected and accelerated (BCa) bootstrap methods were compared for empirical coverage probabilities and expected lengths by the Monte Carlo simulation using the RStudio program with sample sizes of 10, 30, 50, 100, 500, and 1,000. The parameter values were set at 0.1, 0.3, 0.5, 0.8, 1, 1.5, and 2 with 1,000 replications. The simulation results suggested that the bootstrap-based CIs required improvement to attain the nominal confidence level for small sample sizes. No significant differences were detected in the performances of bootstrap-based CIs when evaluating large sample sizes, with the BCa bootstrap CI exhibiting superior performance compared to the others. The application of bootstrap-based CIs to meteorological data yielded comparable results to the simulation study.
Downloads
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
References
Ahmad, A., Jallal, M., Mudasir, S., Ahmad, A., & Tripathi, R. (2021). The discrete Poisson-Rani distribution with properties and applications. International Journal of Open Problems in Computer Science and Mathematics, 14(3), 63–78.
Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6), 716–723. https://doi.org/10.1109/TAC.1974.1100705
Brammer, H. (2020). Problems with analysing meteorological data for assessing climate change: Examples from Bangladesh. International Journal of Environmental Studies, 77(6), 905–915. https://doi.org/10.1080/00207233.2020.1848763
Canty, A., & Ripley, B. (2022). Boot: Bootstrap R (S-Plus) functions (R Package Version 1.3-28.1) [Computer software]. Comprehensive R Archive Network (CRAN). https://CRAN.R-project.org/package=boot
Chernick, M. R., & LaBudde, R. A. (2011). An introduction to bootstrap methods with applications to R. John Wiley & Sons.
Clarke, B., Otto, F., Stuart-Smith, R., & Harrington, L. (2022). Extreme weather impacts of climate change: An attribution perspective. Environmental Research: Climate, 1(1), Article 012001. https://doi.org/10.1088/2752-5295/ac6e7d
Davison, A. C., & Hinkley, D. V. (1997). Bootstrap methods and their application. Cambridge University Press.
Efron, B. (1982). The jackknife, the bootstrap, and other resampling plans. SIAM.
Henningsen, A., & Toomet, O. (2011). maxLik: A package for maximum likelihood estimation in R. Computational Statistics, 26(3), 443–458. https://doi.org/10.1007/s00180-010-0217-1
Kirby, K. N., & Gerlanc, D. (2013). BootES: An R package for bootstrap confidence intervals on effect sizes. Behavior Research Methods, 45(4), 905–927. https://doi.org/10.3758/s13428-013-0330-5
Kissell, R., & Poserina, J. (2017). Optimal sports math, statistics, and fantasy. Academic Press.
Kostyshak, S. (2022). Bootstrap: Functions for the book an introduction to the bootstrap (R package version 2019.6) [Computer software] Comprehensive R Archive Network (CRAN). https://CRAN.R-project.org/package=bootstrap
Lindley, D. V. (1958). Fiducial distributions and Bayes’ theorem. Journal of the Royal Statistical Society Series B: Statistical Methodology, 20(1), 102–107. https://doi.org/10.1111/j.2517-6161.1958.tb00278.x
Meeker, W. Q., Hahn, G. J., & Escobar, L. A. (2017). Statistical intervals: A guide for practitioners and researchers. John Wiley & Sons.
Murphy, M. V. (2022). semEff: Automatic calculation of effects for piecewise structural equation models (R Package Version 0.6.1) [Computer software] Comprehensive R Archive Network (CRAN). https://CRAN.R-project.org/package=semEff
Nwry, A. W., Kareem, H. M., Ibrahim, R. B., & Mohammed, S. M. (2021). Comparison between bisection, Newton and secant methods for determining the root of the non-linear equation using MATLAB. Turkish Journal of Computer and Mathematics Education, 12(14), 1115–1122.
Ong, S.-H., Low, Y.-C., & Toh, K.-K. (2021). Recent developments in mixed poisson distributions. ASM Science Journal, 14. https://doi.org/10.32802/asmscj.2020.464
RStudio Team. (2021). RStudio: Integrated development for R. [Computer software]. RStudio, PBC.
Sankaran, M. (1970). The discrete Poisson-Lindley distribution. Biometrics, 26(1), 145–149. https://doi.org/10.2307/2529053
Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6(2), 461–464. http://www.jstor.org/stable/2958889
Shanker, R. (2015a). Akash distribution and its applications. International Journal of Probability and Statistics, 4(3), 65–75. https://doi.org/10.5923/j.ijps.20150403.01
Shanker, R. (2015b). Shanker distribution and its applications. International Journal of Statistics and Applications, 5(6), 338–348. https://doi.org/10.5923/j.statistics.20150506.08
Shanker, R. (2016a). Amarendra distribution and its applications. American Journal of Mathematics and Statistics, 6(1), 44–56. https://doi.org/10.5923/j.ajms.20160601.05
Shanker, R. (2016b). Aradhana distribution and its applications. International Journal of Statistics and Applications, 6(1), 23–34. https://doi.org/10.5923/j.statistics.20160601.04
Shanker, R. (2016c). Sujatha distribution and its applications. Statistics in Transition. New Series, 17(3), 391–410. https://doi.org/10.21307/stattrans-2016-029
Shanker, R. (2016d). Devya distribution and its applications. International Journal of Statistics and Applications, 6(4), 189–202. https://doi.org/10.5923/j.statistics.20160604.01
Shanker, R. (2016e). The discrete Poisson-Sujatha distribution. International Journal of Probability and Statistics, 5(1), 1–9. https://doi.org/10.5923/j.ijps.20160501.01
Shanker, R. (2017a). The discrete Poisson-Akash distribution. International Journal of Probability and Statistics, 6(1), 1–10. https://doi.org/10.5923/j.ijps.20170601.01
Shanker, R. (2017b). Rani distribution and its application. Biometrics & Biostatistics International Journal, 6(1), 256–265. https://doi.org/10.15406/bbij.2017.06.00155
Shanker, R. (2017c). Rama distribution and its application. International Journal of Statistics and Applications, 7(1), 26–35. https://doi.org/10.5923/j.statistics.20170701.04
Shanker, R. (2017d). Akshaya distribution and its application. American Journal of Mathematics and Statistics, 7(2), 51–59. https://doi.org/10.5923/j.ajms.20170702.01
Shanker, R., Fesshaye, H., Shanker, R., Leonida, T. A., & Sium, S. (2017). On discrete Poisson-Shanker distribution and its applications. Biometrics & Biostatistics International Journal, 5(1), 6–14. https://doi.org/10.15406/bbij.2017.05.00121
Shukla, K. K., & Shanker, R. (2019). The discrete Poisson-Ishita distribution . International Journal of Statistics & Economics, 20(2), 109–122.
Shukla, K. K., & Shanker, R. (2020). The Poisson-Prakaamy distribution and its applications. Aligarh Journal of Statistics, 40, 137–150.
Sukkasem, J. (2010). The modified Kolmogorov-Smirnov one-sample test statistic. Thailand Statistician, 8(2), 143–155. https://ph02.tci-thaijo.org/index.php/thaistat/article/view/34284
Tan, S. H., & Tan, S. B. (2010). The correct interpretation of confidence intervals. Proceedings of Singapore Healthcare, 19(3), 276–278. https://doi.org/10.1177/201010581001900316
Tharshan, R., & Wijekoon, P. (2022). A new mixed Poisson distribution for over-dispersed count data: Theory and applications. Reliability: Theory and Applications, 17(1), 33–51. https://doi.org/10.24412/1932-2321-2022-167-33-51
Ukoumunne, O. C., Davison, A. C., Gulliford, M. C., & Chinn, S. (2003). Non-parametric bootstrap confidence intervals for the intraclass correlation coefficient. Statistics in Medicine, 22(24), 3805–3821. https://doi.org/10.1002/sim.1643
van den Boogaard, H. F. P., & Hall, M. J. (2004). The construction of confidence intervals for frequency analysis using resampling techniques: A supplementary note. Hydrology and Earth System Sciences, 8(6), 1174–1178. https://doi.org/10.5194/hess-8-1174-2004
Wasinrat, S., & Choopradit, B. (2023). The poisson inverse Pareto distribution and its application. Thailand Statistician, 21(1), 110–124. https://ph02.tci-thaijo.org/index.php/thaistat/article/view/248027
Wilcox, R. R. (2021). Introduction to robust estimation and hypothesis testing (5th ed.). Academic Press.
Zhang, B., Cai, D., Ai, S., Wang, H., & Zuo, X. (2023). Research on the influencing factors and prevention measures of long-term forest fire risk in Northeast China. Ecological Indicators, 155, Article 110965. https://doi.org/10.1016/j.ecolind.2023.110965
