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

Abstract

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.