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A stochastic evolutionary model generating a mixture of exponential distributions

Author

Listed:
  • Trevor Fenner

    (Birkbeck, University of London)

  • Mark Levene

    (Birkbeck, University of London)

  • George Loizou

    (Birkbeck, University of London)

Abstract

Recent interest in human dynamics has stimulated the investigation of the stochastic processes that explain human behaviour in various contexts, such as mobile phone networks and social media. In this paper, we extend the stochastic urn-based model proposed in [T. Fenner, M. Levene, G. Loizou, J. Stat. Mech. 2015, P08015 (2015)] so that it can generate mixture models, in particular, a mixture of exponential distributions. The model is designed to capture the dynamics of survival analysis, traditionally employed in clinical trials, reliability analysis in engineering, and more recently in the analysis of large data sets recording human dynamics. The mixture modelling approach, which is relatively simple and well understood, is very effective in capturing heterogeneity in data. We provide empirical evidence for the validity of the model, using a data set of popular search engine queries collected over a period of 114 months. We show that the survival function of these queries is closely matched by the exponential mixture solution for our model.

Suggested Citation

  • Trevor Fenner & Mark Levene & George Loizou, 2016. "A stochastic evolutionary model generating a mixture of exponential distributions," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 89(2), pages 1-7, February.
    • Handle: RePEc:spr:eurphb:v:89:y:2016:i:2:d:10.1140_epjb_e2016-60926-8
    DOI: 10.1140/epjb/e2016-60926-8
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    References listed on IDEAS

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    1. Maxim Finkelstein, 2008. "Failure Rate Modelling for Reliability and Risk," Springer Series in Reliability Engineering, Springer, number 978-1-84800-986-8, September.
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    Cited by:

    1. Levene, Mark & Fenner, Trevor, 2021. "A stochastic differential equation approach to the analysis of the 2017 and 2019 UK general election polls," International Journal of Forecasting, Elsevier, vol. 37(3), pages 1227-1234.

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