Long-tailed distributions of inter-event times as mixtures of exponential distributions

Abstract

Inter-event times of various human behavior are apparently non-Poissonian and obey long-tailed distributions as opposed to exponential distributions, which correspond to Poisson processes. It has been suggested that human individuals may switch between different states in each of which they are regarded to generate events obeying a Poisson process. If this is the case, inter-event times should approximately obey a mixture of exponential distributions with different parameter values. In the present study, we introduce the minimum description length principle to compare mixtures of exponential distributions with different numbers of components (i.e., constituent exponential distributions). Because these distributions violate the identifiability property, one is mathematically not allowed to apply the Akaike or Bayes information criteria to their maximum likelihood estimator to carry out model selection. We overcome this theoretical barrier by applying a minimum description principle to joint likelihoods of the data and latent variables. We show that mixtures of exponential distributions with a few components are selected as opposed to more complex mixtures in various data sets and that the fitting accuracy is comparable to that of state-of-the-art algorithms to fit power-law distributions to data. Our results lend support to Poissonian explanations of apparently non-Poissonian human behavior.

arXiv comment2 figures, 4 tables, SI and code are available here: https://github.com/naokimas/exp_mixture_model

References in corpus (17)

• Power-law distributions in empirical data
• Power laws, Pareto distributions and Zipf's law
• Temporal Networks
• The origin of bursts and heavy tails in human dynamics
• Powerlaw: a Python package for analysis of heavy-tailed distributions
• Scale-free networks are rare
• What's in a crowd? Analysis of face-to-face behavioral networks
• Modeling bursts and heavy tails in human dynamics
• A Poissonian explanation for heavy-tails in e-mail communication
• Information dynamics shape the networks of Internet-mediated prostitution
• Data on face-to-face contacts in an office building suggests a low-cost vaccination strategy based on community linkers
• On Universality in Human Correspondence Activity
• Scale-free Networks Well Done
• A Gillespie algorithm for non-Markovian stochastic processes
• Modelling bursty time series
• Self-exciting point process modeling of conversation event sequences
• Two-state Markov-chain Poisson nature of individual cellphone call statistics

Cited by in corpus (6)

• Gillespie algorithms for stochastic multiagent dynamics in populations and network
• Small inter-event times govern epidemic spreading on temporal networks
• Generative models of simultaneously heavy-tailed distributions of inter-event times on nodes and edges
• Maximum Entropy approach to multivariate time series randomization
• Metapopulation models imply non-Poissonian statistics of interevent times
• Spline tie-decay temporal networks