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Related Experiment Video

Updated: Feb 7, 2026

Sampling Blood from the Lateral Tail Vein of the Rat

Sampling Blood from the Lateral Tail Vein of the Rat

Published on: May 18, 2015

Multiple outlier detection in samples with exponential & Pareto tails.

Didier Sornette¹, Ran Wei²

¹Institute of Risk Analysis, Prediction and Management, Southern University of Science and Technology, Shenzhen, People's Republic of China.

Journal of Applied Statistics

|February 6, 2026

Summary

We developed new robust statistics (MRS and SRS) for outlier detection in heavy-tailed data. These methods improve resistance to masking and swamping, making sequential testing competitive again.

Keywords:

Dragon King Outlier detection Pareto sample exponential sample extreme value theory

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Last Updated: Feb 7, 2026

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Area of Science:

Statistics
Data Analysis

Background:

Outlier detection is crucial in analyzing heavy-tailed data (e.g., exponential, Pareto).
Traditional methods struggle with masking and swamping, particularly in sequential testing.
Inward sequential testing has been overshadowed by outward testing due to these limitations.

Purpose of the Study:

Introduce novel robust test statistics, max-robust-sum (MRS) and sum-robust-sum (SRS).
Enhance outlier detection robustness in samples with exponential or Pareto tails.
Re-establish inward sequential testing as a viable alternative to outward testing.

Main Methods:

Developed two ratio-based robust test statistics: MRS and SRS.
Statistics compare largest suspected outliers to a trimmed partial sample sum.
Derived analytical null distributions and conducted simulations for performance comparison.

Main Results:

MRS and SRS demonstrate improved resistance to masking and swamping.
Proposed tests significantly reduce the masking problem in inward sequential testing.
Performance was evaluated against classical statistics across various data scenarios.

Conclusions:

MRS and SRS offer a robust approach to outlier detection in heavy-tailed distributions.
Inward sequential testing is re-established as a competitive method without multiple testing correction.
The 'Dragon King' concept was applied to significant outliers in diverse case studies.