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 NIWITPONG^2,* & 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

Received: 22 November 2022/Accepted: 24 October 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

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*Corresponding author; email: sa-aat.n@sci.kmutnb.ac.th