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