Dragon-kings: mechanisms, statistical methods and empirical evidence

TL;DR

This paper reviews the concept of dragon-kings, discussing their mechanisms, methods for detection, and empirical evidence across various systems, highlighting recent advances and ongoing challenges in understanding these extreme events.

Contribution

It provides a comprehensive overview of mechanisms, statistical detection methods, and empirical evidence for dragon-kings, advancing understanding in this complex field.

Findings

Significant progress in identifying mechanisms of dragon-kings

Development of novel statistical tests for detection

Empirical evidence of dragon-kings in diverse systems

Abstract

This introductory article presents the special Discussion and Debate volume "From black swans to dragon-kings, is there life beyond power laws?" published in Eur. Phys. J. Special Topics in May 2012. We summarize and put in perspective the contributions into three main themes: (i) mechanisms for dragon-kings, (ii) detection of dragon-kings and statistical tests and (iii) empirical evidence in a large variety of natural and social systems. Overall, we are pleased to witness significant advances both in the introduction and clarification of underlying mechanisms and in the development of novel efficient tests that demonstrate clear evidence for the presence of dragon-kings in many systems. However, this positive view should be balanced by the fact that this remains a very delicate and difficult field, if only due to the scarcity of data as well as the extraordinary important implications with respect to hazard assessment, risk control and predictability.