Sains Malaysiana 41(6)(2012): 769-778

On Discordance Test for the Wrapped Normal Data

(Ujian Tak Sejajar bagi Data Normal Balutan)

Adzhar Rambli¹, Mohd Ikhwan Abdulah¹, Safwati Ibrahim¹, Abdul Ghapor Hussin² & Ibrahim Mohamed¹*

¹Institute of Mathematical Sciences University of Malaya, Kuala Lumpur, Malaysia

²Centre for Foundation studies in Sciences, University of Malaya, Kuala Lumpur, Malaysia

Diserahkan: 7 Julai 2011 / Diterima: 30 Disember 2011

ABSTRACT

This paper focuses on detecting outliers in the circular data which follow the wrapped normal distribution. We considered four discordance tests based on M, C, D and A statistics. The cut-off points of the four tests were obtained and the performance of the detection procedures was studied via simulations. In general, we showed that the discordance test based on the A statistic outperforms the other tests in all cases. For illustration, the city of Kuantan wind direction data set was considered.

Keywords: A statistics; circular; discordance; outlier; wrapped normal distribution

ABSTRAK

Kajian ini tertumpu kepada pengesanan nilai tersisih yang wujud di dalam data bulatan terutamanya data bertaburan normal balutan. Empat ujian sejajar berdasarkan statistik seperti M, C, D dan A dipertimbangkan. Titik potongan dan prestasi prosedurbagi mengesan nilai tersisih diperoleh melalui kajian simulasi. Secara amnya, dibuktikan bahawa ujian tak sejajar berdasarkan statistik A adalah lebih baik berbanding statistik yang lain untuk kesemua kes. Sebagai contoh, data arah angin bandar Kuantan telah digunakan sebagai contoh.

Kata kunci: Bulatan; nilai tersisih; statistik A; taburan normal balutan

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*Pengarang surat-menyurat, email: imohamed@um.edu.my