Sains Malaysiana 54(8)(2025): 2099-2112

http://doi.org/10.17576/jsm-2025-5408-18

 

A Comparative Analysis of Stratified Double Folded Ranked Set Sampling Performance Across Various Distributions

 (Analisis Perbandingan Prestasi Persampelan Set Berperingkat Berlipat Ganda Berstrata Melalui Pelbagai Taburan)

 

CHAINARONG PEANPAILOON¹ & NOPPAKUN THONGMUAL^2,*

 

¹Department of Curriculum and Instruction (Mathematics), Faculty of Education,

Sakon Nakhon Rajabhat University, Sakon Nakhon 47000, Thailand

²Faculty of Sciences, Department of Science and Mathematics, Kalasin University, 46000, Thailand

 

Diserahkan: 2 Oktober 2024/Diterima: 25 Jun 2025

 

Abstract

Efficient statistical estimation is crucial for accurate population parameter estimation. This study introduces and evaluates Stratified Double Folded Ranked Set Sampling (SDFRSS), a modified sampling technique designed to enhance estimation efficiency across various probability distributions. Using Monte Carlo simulations, SDFRSS is compared with Stratified Simple Random Sampling (SSRS), Stratified Ranked Set Sampling (SRSS), and Stratified Median Ranked Set Sampling (SMRSS) based on Mean Squared Error (MSE) and Relative Efficiency (RE) under multiple distributions, including Normal, Student’s t, Uniform, Exponential, Geometric, Gamma, Beta, Weibull, Log-Normal, Logistic, and Chi-Square. The results showed that SDFRSS consistently outperforms SSRS, SRSS, and SMRSS, particularly in skewed and heavy-tailed distributions, by achieving lower MSE and higher efficiency. It effectively reduces estimation errors while maintaining robustness across different sample sizes and stratification structures. However, for some symmetric distributions, SDFRSS does not always yield the lowest MSE, emphasizing the need for distribution-specific selection of sampling methods. Despite increased computational complexity, SDFRSS provides significant gains in precision and efficiency, making it a valuable tool for researchers in fields requiring accurate statistical estimation. Future research should explore its application in high-dimensional data and real-world statistical problems to further establish its practical utility.

Keywords: Stratified Double Folded Ranked Set Sampling; Stratified Median Ranked Set Sampling; Stratified Ranked Set Sampling; Stratified Simple Random Sampling

 

Abstrak

Anggaran statistik yang cekap adalah penting untuk anggaran parameter populasi yang tepat. Kajian ini memperkenal dan menilai Persampelan Set Berperingkat Berlipat Ganda Berstrata (SDFRSS), teknik persampelan terubah suai yang direka untuk meningkatkan kecekapan anggaran merentas pelbagai taburan kebarangkalian. Menggunakan simulasi Monte Carlo, SDFRSS dibandingkan dengan Persampelan Rawak Mudah Berstrata (SSRS), Persampelan Set Peringkat Berstrata (SRSS) dan Persampelan Set Peringkat Median Berstrata (SMRSS) berdasarkan Ralat Purata Kuasa Dua (MSE) dan Kecekapan Relatif (RE) di bawah berbilang pengagihan, termasuk Normal, t Pelajar, Seragam, Eksponen, Geometri, Gamma, Beta, Weibull, Log-Normal, Logistik dan Khi Kuasa Dua. Keputusan ini menunjukkan bahawa SDFRSS secara tekal mengatasi prestasi SSRS, SRSS dan SMRSS, terutamanya dalam pengedaran condong dan berat, dengan mencapai MSE yang lebih rendah dan kecekapan yang lebih tinggi. Ia berkesan mengurangkan ralat anggaran sambil mengekalkan keteguhan melalui saiz sampel yang berbeza dan struktur stratifikasi. Walau bagaimanapun, untuk sesetengah taburan simetri, SDFRSS tidak selalu menghasilkan MSE terendah, menekankan keperluan untuk pemilihan kaedah pensampelan khusus pengedaran. Walaupun kerumitan pengiraan meningkat, SDFRSS memberikan keputusan yang lebih baik dalam ketepatan dan kecekapan, menjadikannya alatan penting untuk penyelidik dalam bidang yang memerlukan anggaran statistik yang tepat. Penyelidikan masa depan harus meneroka pengaplikasiannya dalam data berdimensi tinggi dan masalah statistik dunia nyata untuk terus mewujudkan utiliti praktikalnya.

Kata kunci: Persampelan Set Kedudukan Berlipat Ganda Berstrata; Persampelan Set Kedudukan Median Berstrata; Persampelan Set Kedudukan Berstrata; Persampelan Rawak Mudah Berstrata

 

RUJUKAN

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Takahasi, K. & Wakimoto, K. 1968. On unbiased estimates of the population mean based on the sample stratified by means of ordering. Ann. Inst. Stat. Math. 20: 1-31.

 

*Pengarang untuk surat-menyurat; email: nop_stat@hotmail.com