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

Received: 7 July 2011 / Accepted: 30 December 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 sepertiM, 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 statistikA 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; statistikA; taburan normal balutan

REFERENCES

Abuzaid, A.H., Mohamed, I.B. & Hussin, A.G. 2009. A new test of discordancy in circular data. Communication in Statistics-Simulation and Computation 38(4): 682-691.

Barnett, V. & Lewis, T. 1984. Outliers in Statistical Data. New York: John Wiley & Sons.

Collet, D. 1980. Outliers in circular data. Applied Statistics 29: 50-57.

Collet, D. & Lewis, T. 1981. Discriminating between the von Mises and wrapped normal distributions. Australian Journal Statistics 23(1): 73-79.

David, H.A. 1970. Order Statistics. New York and London: Wiley.

Fisher, N.I. 1993. Statistical Analysis of Circular Data. London: Cambridge University Press.

Jammalamadaka, S. R. & SenGupta, A. 2001. Topics in Circular Statistics. Singapore: World Scientific Press.

Kendall, D.G. 1974. Hunting quanta. Trans. R. Soc. Lond. A 276: 231-266.

Kent, J.T. 1976. Distributions, Processes and Statistics on “Spheres”. Ph.D. Thesis, University of Cambridge.

Lukacs, E. 1970. Characteristic Functions. Griffin: Publisher

Mardia, K.V. 1972. Statistics of Directional Data. London: Academic Press.

Mardia, K.V. 1975. Statistics of directional data. Journal of the Royal Statistical Society B (37): 349-393.

Pearson, E.S. & Hartley, H.O. 1966. Biometrika Tables of Statisticians. vol. 1, 3rd ed., London: Cambridge University Press.

Rao, J.S. 1969. Some Contributions to the Analysis of Circular Data. Ph.D. thesis, Indian Statistical Institute, Calcutta, India (Unpublished).

Whittaker, E.T. & Watson, G.N. 1944. A Course in Modern Analysis: Cambridge: Cambridge University Press.

*Corresponding author, email: imohamed@um.edu.my