Power laws in the Roman Empire: a survival analysis

Area of Science:

• Historical Demography
• Statistical Modeling
• Ancient History

Background:

• The Roman Empire's enduring legacy is evident in modern institutions.
• Despite adaptable political structures, the Roman Empire experienced frequent internal conflicts.
• A significant number of Roman emperors met violent ends through assassination, suicide, or battle.

Purpose of the Study:

• To statistically analyze patterns in the duration of Roman emperor reigns.
• To develop and apply a novel power-law model for predicting time-to-violent-death among Roman emperors.
• To investigate the presence and implications of power-law distributions in historical survival data.

Main Methods:

• Survival data analysis techniques were employed.
• A dataset of all 175 Roman emperors was compiled.
• A new power-law model with change points was proposed and utilized to analyze censored data and long-term survivors.

Main Results:

• The study identified underlying patterns in the length of Roman emperor reigns.
• The proposed power-law model demonstrated improved predictive accuracy compared to previous models.
• Results confirmed the occurrence of power-law distributions in survival data, mirroring observations in natural and artificial systems.

Conclusions:

• Power-law distributions are a ubiquitous phenomenon, extending to historical survival data.
• The developed statistical approach offers a robust method for analyzing historical reign lengths and violent deaths.
• This methodology has potential applications in studying other ancient civilizations and in fields like engineering and medicine.