Detection of Outliers in Univariate Circular Data Using New Cut-off Points for the Circular Distance

Abstract

The aim of this study is to propose two new cut-off points for outlier detection in univariate circular data using the concept of circular distance. The first cut-off point involves using a quantile of the gamma distribution based on adjusted circular distances, whereas the second cut-off point employs the upper fence of a modified boxplot for skewed data. Simulation studies are conducted using both uncontaminated and contaminated data, and the performance of the proposed cut-off points is evaluated in the proportion of outliers, probability of all outliers being successfully detected, probability of outliers being falsely detected as inliers (masking effect), and probability of inliers detected as outliers (swamping effect). Real data examples are also used to demonstrate the efficacy of the proposed cut-off points. The results of the simulation and real data experiments show that the proposed cut-off point involves using a quantile of the gamma distribution based on adjusted circular distances and is successful in outlier detection compared to the existing cut-off points.