Sains Malaysiana 52(11)(2023): 3273-3292

http://doi.org/10.17576/jsm-2023-5211-19

 

Parametric Bootstrap Confidence Interval Estimation for the Percentile and Difference between the Percentiles of Delta-Lognormal Distributions with Application to Rainfall Data in Thailand

(Anggaran Selang Keyakinan Parametrik Butstrap untuk Persentil dan Perbezaan antara Peratus Taburan Delta-Lognormal dengan Aplikasi pada Data Hujan di Thailand)

 

WARISA THANGJAI1, SA-AAT NIWITPONG2,* & SUPARAT NIWITPONG2

 

1Department of Statistics, Faculty of Science, Ramkhamhaeng University, 10240, Bangkok, Thailand

2Department of Applied Statistics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, 10800, Bangkok, Thailand

 

Diserahkan: 22 November 2022/Diterima: 24 Oktober 2023

 

Abstract

In Thailand, flooding often occurs during the summer monsoon when many tropical storms affect the country. The motivation of this study was to plan for and mitigate the damage caused by flooding in the future. The confidence interval (CI) for the percentile of a precipitation dataset can be used to estimate the intensity of rainfall in a particular area whereas the CI for the difference between the percentiles of two datasets can be used to compare the rainfall intensities in two areas. To this end, the performances of several approaches to estimate the CI for the percentile and difference between the percentiles of delta-lognormal distributions were constructed and compared. These estimates were constructed based on the Bayesian (BS) and parametric bootstrap (PB) approaches, as well as two fiducial generalized confidence interval (FGCI) approaches. The performances of the methods were evaluated using Monte Carlo simulation, the results of which indicate that the PB approach for both CIs performed the best in all scenarios tested. Its suitability was confirmed via two illustrative examples using daily rainfall datasets for Chiang Mai and Lampang provinces in Thailand.

 

Keywords: Bayesian; delta-lognormal; fiducial generalized confidence interval; parametric bootstrap; rainfall

 

Abstrak

Di Thailand, banjir sering berlaku semasa monsun musim panas apabila banyak ribut tropika menjejaskan negara. Motivasi kajian ini adalah untuk merancang dan mengurangkan kerosakan akibat banjir pada masa hadapan. Selang keyakinan (CI) untuk persentil set data titisan boleh digunakan untuk menganggarkan keamatan curahan hujan di kawasan tertentu manakala CI untuk perbezaan antara persentil dua set data boleh digunakan untuk membandingkan keamatan curahan hujan di dua kawasan. Untuk tujuan ini, prestasi beberapa pendekatan untuk menganggarkan CI bagi persentil dan perbezaan antara persentil taburan delta-lognormal telah dibina dan dibandingkan. Anggaran ini telah dibina berdasarkan pendekatan Bayesian (BS) dan parametrik butstrap (PB) serta dua pendekatan selang keyakinan teritlak fidusial (FGCI). Prestasi kaedah telah dinilai menggunakan simulasi Monte Carlo yang hasilnya menunjukkan bahawa pendekatan PB untuk kedua-dua CI menunjukkan prestasi terbaik dalam semua senario yang diuji. Kesesuaiannya disahkan melalui dua contoh ilustrasi menggunakan set data curahan hujan harian untuk wilayah Chiang Mai dan Lampang di Thailand.

 

Kata kunci: Bayesian; curahan hujan; delta-lognormal; parametrik butstrap; selang keyakinan teritlak fidusial

 

RUJUKAN

Aitchison, J. & Brown, J.A.C. 1966. The Lognormal Distribution with Special Reference to Its Uses in Economics. England: Cambridge University Press.

Balakrishnan, N., Hayter, A.J., Liu, W. & Kiatsupaibul, S. 2015. Confidence intervals for quantiles of a two-parameter exponential distribution under progressive type-II censoring. Communications in Statistics - Theory and Methods 44(14): 3001-3010.

Chakraborti, S. & Li, J. 2007. Confidence interval estimation of a normal percentile. The American Statistician 61(4): 331-336.

Chen, S., Li, Y.X., Shin, J.Y. & Kim, T.W. 2016.Constructing confidence intervals of extreme rainfall quantiles using Bayesian, bootstrap, and profile likelihood approaches. Science China Technological Sciences 59: 573-585.

Dunn, P.K. 2001. Bootstrap confidence intervals for predicted rainfall quantiles. International Journal of Climatology 21(1): 89-94.

Hannig, J., Lidong, E., Abdel-Karim, A. & Iyer H. 2006. Simultaneous fiducial generalized confidence intervals for ratios of means of lognormal distributions. Austrian Journal of Statistics 35: 261-269.

Hasan, M.S. & Krishnamoorthy, K. 2018. Confidence intervals for the mean and a percentile based on zero-inflated lognormal data. Journal of Statistical Computation and Simulation 88(8): 1499-1514.

Hayter, A.J. 2014. Simultaneous confidence intervals for several quantiles of an unknown distribution. The American Statistician 68(1): 56-62.

Jaithun, M., Niwitpong, S-A. & Niwitpong, S. 2018. Estimating the difference in the percentiles of two delta-lognormal independent populations. Studies in Computational Intelligence 808: 402-411.

Lu, F., Wang, H., Yan, D.H., Zhang, D.D. & Xiao, W.H. 2013. Application of profile likelihood function to the uncertainty analysis of hydrometeorological extreme inference. Science China Technological Sciences 56: 3151-3160.

Malekzadeh, A. & Jafari, A.A. 2018. Testing equality of quantiles of two-parameter exponential distributions under progressive type II censoring. Journal of Statistical Theory and Practice 12(4): 776-793.

Malekzadeh, A. & Kharrati-Kopaei, M. 2020. Simultaneous confidence intervals for the quantile differences of several two-parameter exponential distributions under the progressive type II censoring scheme. Journal of Statistical Computation and Simulation 90(11): 2037-2056.

Md, A.K., Saleh, E., Hassanein, K.M. & Ali, M.M. 1988. Estimation and testing of hypotheses about the quantile function of the normal distribution. Journal of Information and Optimization Sciences 9(1): 85-98.

Mandel, M. & Betensky, R.A. 2008. Simultaneous confidence intervals based on the percentile bootstrap approach. Computational Statistics and Data Analysis 52: 2158-2165.

Maneerat, P., Nakjai, P. & Niwitpong, S-A. 2022. Bayesian interval estimations for the mean of delta-three parameter lognormal distribution with application to heavy rainfall data. PLoS ONE 17(4): e0266455.

Maneerat, P., Niwitpong, S-A. & Niwitpong, S. 2021. Bayesian confidence intervals for a single mean and the difference between two means of delta-lognormal distributions. Communications in Statistics-Simulation and Computation 50: 2906-2934.

Navruz, G. & Özdemir, A.F. 2018. Quantile estimation and comparing two independent groups with an approach based on percentile bootstrap. Communications in Statistics - Simulation and Computation 47(7): 2119-2138.

Padgett, W.J. & Tomlinson, M.A. 2003. Lower confidence bounds for percentiles of Weibull and Birnbaum-Saunders distributions. Journal of Statistical Computation and Simulation 73(6): 429-443.

Reiss, R.D. & Ruschendorf, L. 1976. On Wilks’ distribution-free confidence intervals for quantile intervals. Journal of the American Statistical Association 71(356): 940-944.

Reis, Jr. D.S. & Stedinger, J.R. 2005. Bayesian MCMC flood frequency analysis with historical information. Journal of Hydrology 313: 97-116.

Serinaldi, F. 2009. Assessing the applicability of fractional order statistics for computing confidence intervals for extreme quantiles. Journal of Hydrology 376: 528-541.

Smith, P. & Sedransk, J. 1983. Lower bounds for confidence coefficients for confidence intervals for finite population quantiles. Communications in Statistics - Theory and Methods 12(12): 1329-1344.

Thangjai, W. & Niwitpong, S. 2022. Bootstrap confidence intervals for common signal-to-noise ratio of two-parameter exponential distributions. Statistics, Optimization and Information Computing 10: 858-872.

Thangjai, W. & Niwitpong, S-A. 2020. Confidence intervals for difference of signal-to-noise ratios of two-parameter exponential distributions. International Journal of Statistics and Applied Mathematics 5(3): 47-54.

Thangjai, W., Niwitpong, S-A. & Niwitpong, S. 2022. Estimation of common percentile of rainfall datasets in Thailand using delta-lognormal distributions. PeerJ 10: e14498.

Thangjai, W., Niwitpong, S-A. & Niwitpong, S. 2020. Confidence intervals for the common coefficient of variation of rainfall in Thailand. PeerJ 8: e10004.

Tian, W., Yang, Y. & Tong, T. 2022. Confidence intervals based on the difference of medians for independent log-normal distributions. Mathematics 10: 2989.

Yosboonruang, N. & Niwitpong, S. 2020. Statistical inference on the ratio of delta-lognormal coefficients of variation. Applied Science and Engineering Progress 14(3): 489-502.

Yosboonruang, N., Niwitpong, S-A. & Niwitpong, S. 2022. Bayesian computation for the common coefficient of variation of delta-lognormal distributions with application to common rainfall dispersion in Thailand. PeerJ 10: e12858.

Yosboonruang, N., Niwitpong, S-A. & Niwitpong, S. 2020. The Bayesian confidence intervals for measuring the difference between dispersions of rainfall in Thailand. PeerJ 8: e9662.

Yosboonruang, N., Niwitpong, S-A. & Niwitpong, S. 2019. Measuring the dispersion of rainfall using Bayesian confidence intervals for coefficient of variation of delta-lognormal distribution: A study from Thailand. PeerJ 7(271): e7344.

Zhang, Q., Xu, J., Zhao, J., Liang, H. & Li, X. 2022. Simultaneous confidence intervals for ratios of means of zero-inflated log-normal populations. Journal of Statistical Computation and Simulation 92(6): 1113-1132.

 

*Pengarang untuk surat-menyurat; email: sa-aat.n@sci.kmutnb.ac.th

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

   

sebelumnya