Empirical Evaluation of the Relative Range for Detecting Outliers

Outlier detection plays a key role in data analysis by improving data quality, uncovering data entry errors, and spotting unusual patterns, such as fraudulent activities. Choosing the right detection method is essential, as some approaches may be too complex or ineffective depending on the data distribution. In this study, we explore a simple yet powerful approach using the range distribution to identify outliers in univariate data. We compare the effectiveness of two range statistics: we normalize the range by the standard deviation (σ) and the interquartile range (IQR) across different types of distributions, including normal, logistic, Laplace, and Weibull distributions, with varying sample sizes (n) and error rates (α). An evaluation of the range behavior across multiple distributions allows for the determination of threshold values for identifying potential outliers. Through extensive experimental work, the accuracy of both statistics in detecting outliers under various contamination strategies, sample sizes, and error rates (α=0.1,0.05,0.01) is investigated. The results demonstrate the flexibility of the proposed statistic, as it adapts well to different underlying distributions and maintains robust detection performance under a variety of conditions. Our findings underscore the value of an adaptive method for reliable anomaly detection in diverse data environments.