Ali H. Abuzaid 0000-0002-6680-7371

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The problem of outlier detection in univariate circular data was the object of increased interest over the last decade. New numerical and graphical methods were developed for samples from different circular probability distributions. The main drawback of the existing methods is, however, that they are distribution-based and ignore the problem of multiple outliers.
The local outlier factor (LOF) is a density-based method for detecting outliers in multivariate data and it depends on the local density of every k nearest neighbours. The aim of this paper is to extend the application of the LOF to the detection of possible outliers in circular samples, where the angles of circular data are represented in two Cartesian coordinates and treated as bivariate data. The performance of the LOF is compared against other existing numerical methods by means of a simulation based on the power of a test and the proportion of correct detection. The LOF performance is compatible with the best existing discordancy tests, while outperforming other tests. The level of the LOF performance is directly related to the contamination and concentration parameters, while having an inverse relationship with the sample size.
In order to illustrate the process, the LOF and other existing discordancy tests are applied to detect possible outliers in two common real circular datasets.


discordancy, distance, multiple outliers, neighbours, spacing theory


ABUZAID, A. H. (2020). Identifying density-based local outliers in medical multivariate circular data. Statistics in Medicine. Vol. 39 (210), pp. 2793-2798.

ABUZAID, A. H., EL-HANJOURI, M. M., and KULLAB, M. M., (2015). On Discordance Tests for the Wrapped Cauchy Distribution, Open Journal of Statistics, Vol. 5 (4), pp. 245-253.

ABUZAID, A. H., MOHAMED, I. B., and HUSSIN, A. G., (2012). Boxplot for Circular Variables. Computational Statistics, Vol. 27 (3), pp. 381-392.

ABUZAID, A. H., RAMBLI, A., and HUSSIN, A.G., (2012). Statistics for a New Test of Discordance in Circular Data. Communications in Statistics - Simulation and Computation, Vol. 41 (10), pp. 1882-1890.

ABUZAID, A. M., MOHAMED, I. B., and HUSSIN, A. G., (2009). A new test of discordancy in circular data. Communications in Statistics-Simulation and Computation, Vol. 38(4), pp. 682-691.

ALKASADI, N. A., IBRAHIM, S. ABUZAID, A. H., and YUSOFF. M. I., (2019). Outliers Detection in Multiple Circular Regression Models Using DFFITc Statistic, Sains Malaysiana, Vol. 48 (7), pp. 1557-1563.

BARNETT, V. AND LEWIS, T., (1984). Outliers in Statistical Data. 2nd ed., John Wiley & Sons, Chichesters.

BREUNIG, M. M., KRIEGEL, H.-P., NG, R. T., and SANDER, JÖ., (2000). LOF: identifying density-based local outliers. ACM sigmod record, pp. 93-104.

COLLETT, D. (1980). Outliers in circular data. Applied Statistics, Vol. 29 (1), pp. 50-57.

DAS, M. K., GOGOI, B., (2015). Procedures of Outlier Detection in Cardioid Distribution, Assam Statistical Review, Vol. 29 (1), pp. 31-45.

FERGUSION, D. E., LANDRETH, H. F., MCKEOWN, J. P., (1967). Sun Compass Orientation of the Northern Cricket Frog. Acris Crepitans. Animal Behavior, Vol. 15, pp. 45-53.

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

MOHAMED, I. B., RAMBLI, A., KHALIDDIN, N., and IBRAHIM, A. I. N., (2016). A New Discordancy Test in Circular Data Using Spacing's Theory, Communications in Statistics - Simulation and Computation, Vol. 45 (8), pp. 2904-2916.

SATARI, S. Z., HUSSIN, A. G, ZUBAIRI, Y. Z., and HASSAN, S. F., (2014). A New Functional Relationship Model For Circular Variables. Pakistan Journal of Statistics, Vol. 30 (3), pp. 397-410.

SIDIK, M. I., RAMBLI, A., MAHMUD, Z., REDZUAN, R. S., and SHAHRI, N., (2019). The Identification of Outliers in Wrapped Normal Data By Using Ga Statistics. International Journal of Innovative Technology and Exploring Engineering, Vol. 8 (4S), pp. 181-189.

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