A comparison on two discordancy tests to detect outlier in von mises (VM) sample

Fatin Najihah Badarisam, Adzhar Rambli, Mohammad Illyas Sidik


This paper focuses on comparing two discordancy tests between robust and non-robust statistic to detect a single outlier in univariate circular data. So far, to the best author knowledge that there is no literature make a comparison between both tests of RCDu Statistic and 𝐺1 Statistic. The test statistics are based on the circular median and spacing theory. In addition, those statistics can detect multiple and patches outliers. The performance tests of RCDu Statistic and 𝐺1 Statistic are tested in outlier proportion of correct detection, masking and swamping effect. At the beginning stage, we obtained the cut-off points for the RCDu Statistic and 𝐺1 Statistic by applying Monte Carlo simulation studies. Then, generated sample from von Mises (VM) with the combination of sample size and concentration parameter. The estimating process of cut-off points for both statistics is repeated 3000 times at 10%, 5% and 1% upper percentiles. As a result, the RCDu Statistic perform well in detecting a correct single outlier. Moreover, the RCDu Statistic has a lower masking rate compared to 𝐺1 Statistic.  However, the 𝐺1 Statistic is better than RCDu Statistic for swamping effect due to a lower swamping rate. Thus, RCDu Statistic performs better than 𝐺1 Statistic in detecting a single outlier for von Mises (VM) sample. As an illustration, both statistics were applied to the real data set from a conducted experiments series to investigate the northen cricket frogs homing ability.


Circular median; Correct detection proportion; Masking; Outliers; RCDu statistic; Spacing theory; Swamping; 𝐺1 statistic

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DOI: http://doi.org/10.11591/ijeecs.v19.i1.pp156-163


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