Outlier labeling via circular boxplot

Boxplot is a simple and flexible graphical tool that has been widely used in exploratory data analysis. Its main application is to identify extreme values and outliers in linear univariate data sets. However, the standard boxplot for linear data set is not suitable to be used for circular data sets due to the bounded property of circular variables. In this paper, we propose and develop a boxplot for circular data sets based on five circular summary statistics which is called circular boxplot. In the process, several problems have been resolved. Firstly, we have overcome the problems of estimating the circular median, the first and second quartiles and overlapping areas between the upper and lower fences. Secondly, we resolve the problem of finding the appropriate boxplot criterion which is (νIQR=1.5IQR) in linear case, where IQR is the interquartiles range and ν is the resistance constant. Through simulation studies, we identify the appropriate values of circular boxplot criterion which depends on the concentration parameter. The power of performances of the proposed boxplot is investigated. We then develop S-Plus subroutines to display the circular boxplot and apply the plot on a real circular data set