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Modelling dynamics of marathons – A mixture model approach

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  • Kwong, Hok Shing
  • Nadarajah, Saralees

Abstract

In this paper, statistical properties of marathon dynamics are studied. We find that changes of velocity in marathons follow an unconventional mechanism; in which the log-change of velocity is highly dependent on current velocity with a complex relationship. The conditional distributions of log-change of velocity exhibit patterns of varying means, variances, and skewnesses; as such, the overall velocity distributions are also found to have departed from Gaussian. We illustrate the mechanism with a finite mixture of generalized linear regressions with varying weights and skew normal errors; and we show that the completion time distribution can be approximated by skewed distributions.

Suggested Citation

  • Kwong, Hok Shing & Nadarajah, Saralees, 2019. "Modelling dynamics of marathons – A mixture model approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    • Handle: RePEc:eee:phsmap:v:534:y:2019:i:c:s037843711930408x
    DOI: 10.1016/j.physa.2019.04.034
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    References listed on IDEAS

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    1. Alvarez-Ramirez, Jose & Rodriguez, Eduardo, 2006. "Scaling properties of marathon races," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(2), pages 509-520.
    2. Zhu, Dongming & Zinde-Walsh, Victoria, 2009. "Properties and estimation of asymmetric exponential power distribution," Journal of Econometrics, Elsevier, vol. 148(1), pages 86-99, January.
    3. Lin, Zhenquan & Meng, Fan, 2018. "Empirical analysis on the runners’ velocity distribution in city marathons," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 533-541.
    4. Alvarez-Ramirez, Jose & Rodriguez, Eduardo & Dagdug, Leonardo, 2007. "Time-correlations in marathon arrival sequences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 380(C), pages 447-454.
    5. Rodriguez, E. & Espinosa-Paredes, G. & Alvarez-Ramirez, J., 2014. "Convection–diffusion effects in marathon race dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 393(C), pages 498-507.
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    2. Guo, Junke & Mohebbi, Amin & Zhang, Tian C., 2022. "Application of general unit hydrograph model for marathon finish time distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).

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