Sains Malaysiana 52(7)(2023): 2139-2148

http://doi.org/10.17576/jsm-2023-5207-19

A Comparison between Two Discordancy Tests to Identify Outlier in Wrapped Normal (WN) Samples

(Perbandingan antara Dua Ujian Percanggahan untuk Mengenal Pasti Data Terpencil dalam Sampel Normal Balutan (WN))

NURISHA MOHD ZULKEFLI¹, ADZHAR RAMBLI ^1,*, MOHAMAD ISMETH KHAN AZHAR SUHAIMI¹, IBRAHIM MOHAMED² & RAIHA SHAZWEEN REDZUAN³

¹School of Mathematical Sciences, College of Computing, Informatics and Mathematics,

Universiti Teknologi MARA, 40450 Shah Alam, Selangor, Malaysia

²Institute of Mathematical Sciences, Universiti Malaya, 50603 Kuala Lumpur, Malaysia

³Centre for Foundation Studies in Science, Universiti Malaya, 50603 Kuala Lumpur,

Malaysia

Received: 17 March 2023/Accepted: 6 July 2023

Abstract

This study focuses on comparing the performance of the Robust Circular Distance (RCDU*) (simplified version) and A statistics in detecting a single outlier in the Wrapped Normal (WN) samples. Firstly, this study proposes a simplified version of RCDU statistic. Then, the paper generates the cut-off points for both statistics taken from WN samples via a simulation study. This study also evaluates the performance of both statistics using the proportion of a correct outlier detection. As a result, for a small sample size, the performance of RCDU* and A statistics do not have a huge difference. However, for a large sample size of n=250, A statistic performs slightly better than RCDU* statistic. As an illustration of a practical example, both statistics successfully detected one outlier present in the wind direction data at Kota Bharu station.

Keywords: Circular data; discordancy tests; outliers; wrapped normal distribution

Abstrak

Kajian ini memfokuskan kepada perbandingan prestasi Jarak Berkeliling Teguh (RCDU*) (versi ringkas) dan statistik A dalam mengesan satu data terpencil dalam sampel Normal Balutan (WN). Pertama, kajian ini mencadangkan versi ringkas statistik RCDU. Kemudian, kertas itu menjana titik potong untuk kedua-dua statistik yang diambil daripada sampel WN melalui kajian simulasi. Kajian ini juga menilai prestasi kedua-dua statistik menggunakan perkadaran pengesanan data terpencil yang betul. Akibatnya, untuk saiz sampel yang kecil, prestasi RCDU* dan statistik A tidak mempunyai perbezaan yang besar. Walau bagaimanapun, untuk saiz sampel yang besar n=250, statistik A menunjukkan prestasi yang lebih baik sedikit daripada statistik RCDU*. Sebagai ilustrasi contoh praktikal, kedua-dua statistik berjaya mengesan satu data terpencil hadir dalam data arah angin di stesen Kota Bharu.

Kata kunci: Data pekeliling; data terpencil; taburan normal balutan; ujian percanggahan

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*Corresponding author; email: adzhar@uitm.edu.my