Sains Malaysiana 52(6)(2023): 1879-1888
http://doi.org/10.17576/jsm-2023-5206-22
Bootstrap Methods
for Estimating the Confidence Interval for the Parameter of the Zero-Truncated
Poisson-Sujatha
Distribution and Their Applications
(Kaedah Bootstrap untuk Menganggar Selang Keyakinan untuk Parameter Taburan Poisson-Sujatha Terpangkas Sifar dan Aplikasinya)
WARARIT
PANICHKITKOSOLKUL*
Department of
Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, 12121 Pathumthani,
Thailand
Received: 29
December 2022/Accepted: 12 June 2023
Abstract
Numerous phenomena involve count
data containing non-zero values and the zero-truncated
Poisson-Sujatha distribution can be
used to model such data. However, the confidence interval estimation of its parameter has not yet been examined. In
this study, 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 interval 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,
the bias-corrected and accelerated bootstrap approach
outperformed the others, even for small
sample sizes. Last, the bootstrap methods were used to
calculate the confidence interval for the zero-truncated Poisson-Sujatha parameter via three numerical examples, the results
of which match those from the simulation study.
Keywords: Bootstrap
interval; count data; interval estimation; Poisson-Sujatha
distribution; simulation
Abstrak
Banyak fenomena melibatkan data bilangan yang mengandungi nilai bukan sifar dan taburan Poisson-Sujatha terpangkas sifar boleh digunakan untuk memodelkan data tersebut. Walau bagaimanapun, anggaran selang keyakinan parameternya masih belum diperiksa. Dalam kajian ini, anggaran selang keyakinan berdasarkan kaedah persentil, mudah, pembetulan berat sebelah dan dipercepatkan, serta selang bootstrap-t, telah diperiksa dari segi kebarangkalian liputan dan panjang selang purata melalui simulasi Monte Carlo. Keputusan menunjukkan bahawa mencapai tahap keyakinan nominal menggunakan kaedah bootstrap tidak mungkin untuk saiz sampel yang kecil tanpa mengira tetapan lain. Selain itu, apabila saiz sampel adalah besar, prestasi kaedah tidak jauh berbeza. Secara keseluruhannya, pendekatan bootstrap yang diperbetulkan berat sebelah dan dipercepatkan mengatasi prestasi yang lain, walaupun untuk saiz sampel yang kecil. Terakhir, kaedah bootstrap digunakan untuk mengira selang keyakinan bagi parameter
Poisson-Sujatha terpangkas sifar melalui tiga contoh berangka, yang hasilnya sepadan dengan kajian simulasi.
Kata kunci: Anggaran selang; data bilangan; selang Bootstrap; simulasi; taburan Poisson-Sujatha
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*Corresponding
author; email: wararit@mathstat.sci.tu.ac.th
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