OJS  Vol.5 No.4 , June 2015
On Discordance Tests for the Wrapped Cau-chy Distribution
Abstract: Circular data as any other types of data are subjected to contamination with some unexpected observations which are known outliers. In this paper, four tests of discordancy for circular data based on M, C, D, and A statistics are extended to the wrapped Cauchy distribution to detect possible outliers. The cut-off points and the power of performances are investigated via extensive simulation study. Results show that tests perform better as the concentration of the samples is increased. Two real circular data sets are analysed for illustration.
Cite this paper: Abuzaid, A. , El-hanjouri, M. and Kulab, M. (2015) On Discordance Tests for the Wrapped Cau-chy Distribution. Open Journal of Statistics, 5, 245-253. doi: 10.4236/ojs.2015.54026.

[1]   Jammalamadaka, S.R. and Sengupta, A. (2001) Topics in Circular Statistics. World Scientific Press, Singapore.

[2]   Collett, D. (1980) Outliers in Circular Data. Applied Statistics, 29, 50-57.

[3]   Hussin, A.G., Abuzaid, A., Zulkifili, F. and Mohamed, I. (2010) Asymptotic Covariance ad Detection of Influential Observations in a Linear Functional Relationship Model for Circular Data with Application to the Measurements of Wind Directions. Science Asia, 36, 249-253.

[4]   Abuzaid, A.H., Mohamed, I.B. and Hussin, A.G. (2012) Boxplot for Circular Variables. Computational Statistics, 27, 381-392.

[5]   Rambli, A., Mohamed, I., Hussin, A.G. and Ibrahim, S. (2012) On Discordance Test for the Wrapped Normal Data, Sains Malaysiana, 41, 769-778.

[6]   Ibrahim, S., Rambli, A., Hussin, A.G. and Mohamed, I. (2013) Outlier Detection in a Circular Regression Model Using COVRATIO Statistic. Communications in Statistics - Simulation and Computation, 42, 2272-2280.

[7]   Abuzaid, A.H., Mohamed, I.B. and Hussin, A.G. (2014) Procedures for Outlier Detection in Circular Time Series Models. Environmental and Ecological Statistics, 21, 793-809.

[8]   Lévy, P. (1939) L’addition des variables aléatoires définies sur une circonférence. Bulletin de la Société Mathématique de France, 67, 1-41.

[9]   McCullagh, P. (1996) Möbius Transformation and Cauchy Parameter Estimation. Annals of Statistics, 24, 787-808.

[10]   Fisher, N.I. (1993) Statistical Analysis of Circular Data. Cambridge University Press, London.

[11]   Mardia, K.V. and Jupp, P.E. (2000) Directional Statistics. John Wiley & Sons, London.

[12]   Mardia, K.V. (1975) Statistics of Directional Data. Journal of the Royal Statistical Society, Series B, 37, 349-393.

[13]   Rao, J.S. (1969) Some Contributions to the Analysis of Circular Data. Ph.D. Thesis, Indian Statistical Institute, Calcutta.

[14]   Abuzaid, A.H., Mohamed, I.B. and Hussin, A.G. (2009) A New Test of Discordancy in Circular Data. Communications in Statistics—Simulation and Computation, 38, 682-691.

[15]   Abuzaid, A.H., Hussin, A.G., Rambli, A. and Mohamed, I.B (2012) Statistics for a New Test of Discordance in Circular Data. Communications in Statistics—Simulation and Computation, 41, 1882-1890.

[16]   David, H.A. (1970) Order Statistics. Wiley, New York and London.

[17]   Barnett, V. and Lewis, T. (1984) Outliers in Statistical Data. 2nd Edition, John Wiley & Sons, Chichester.

[18]   Jander, R. (1957) Die optische Richtungsorientierung der Roten Waldameise (Formica rufa L.) Zeitschrift tiir vergMehende Physiologie Bd, 40, 162-238.

[19]   Ravindran, P. and Ghosh, S.K. (2012) Bayesian Analysis of Circular Data Using Wrapped Distributions. Journal of Statistical Theory and Practice, 5, 547-561.

[20]   Kato, S., Shimizu, K. and Shieh, G.S. (2008) A Circular-Circular Regression Model. Statistica Sinica, 18, 633-643.