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