Stationarity of the inter-event power-law distributions

TL;DR

This paper investigates the bursty nature of human activity patterns, revealing that the distribution of inter-event times remains consistent regardless of daily cycles, indicating an intrinsic scheduling pattern.

Contribution

It demonstrates that the inter-event time distribution in human activities is stationary and independent of circadian influences, based on analysis of Wikipedia edits and Twitter posts.

Findings

Inter-event times follow a fat-tailed distribution.

Conditional probability of activity is independent of time of day.

Human scheduling patterns are intrinsic and robust.

Abstract

A number of human activities exhibit a bursty pattern, namely periods of very high activity that are followed by rest periods. Records of these processes generate time series of events whose inter-event times follow a probability distribution that displays a fat tail. The grounds for such phenomenon are not yet clearly understood. In the present work we use the freely available Wikipedia editing records to unravel some features of this phenomenon. We show that even though the probability to start editing is conditioned by the circadian 24 hour cycle, the conditional probability for the time interval between successive edits at a given time of the day is independent from the latter. We confirm our findings with the activity of posting on the social network Twitter. Our result suggests there is an intrinsic humankind scheduling pattern: after overcoming the encumbrance to start an activity, there is a robust distribution of new related actions, which does not depend on the time of day.