Empirical Evaluation of the Relative Range for Detecting Outliers

Area of Science:

• Data Science
• Statistical Analysis
• Machine Learning

Background:

• Outlier detection is crucial for data quality and identifying anomalies like fraud.
• Existing methods can be complex or inefficient depending on data distribution.
• Univariate outlier detection requires robust and adaptable statistical approaches.

Purpose of the Study:

• To explore a simple yet effective range distribution method for univariate outlier detection.
• To compare the performance of range statistics normalized by standard deviation (σ) and interquartile range (IQR).
• To determine optimal threshold values for outlier identification across diverse distributions.

Main Methods:

• Investigated outlier detection using normalized range statistics (range/σ and range/IQR).
• Evaluated performance across normal, logistic, Laplace, and Weibull distributions.
• Tested with varying sample sizes (n) and error rates (α=0.1, 0.05, 0.01) under different contamination strategies.

Main Results:

• The proposed range-based statistics demonstrated flexibility and robustness in outlier detection.
• Performance was consistent across different data distributions and sample sizes.
• Effective threshold values were determined for reliable anomaly identification.

Conclusions:

• A simple, adaptive range distribution method offers reliable outlier detection for univariate data.
• The approach is suitable for diverse data environments and maintains detection accuracy.
• This method enhances data analysis by improving data quality and uncovering unusual patterns.