Relative range for skewed distributions: a tool for outlier detection

Abstract

The ongoing exploration of outlier detection involves the development and refinement of diverse statistical analysis procedures. In this paper, we examine the performance of the standardized range and relative range in detecting outliers in a skewed data. The proposed approach considers Weibull distribution as a placeholder for skewed data. The empirical construction of the PDFs of the standardized range and relative range from the Weibull distribution along with the simulation work for outlier detection reveal that while the relative range possesses comparable probability behavior to the standardized range, it outperforms the standardized range in detecting outliers from skewed data. Furthermore, the simulated outlier detection framework has been applied to real datasets. The results showed that relative range continue to outperform standardised range in identifying outliers.