Modelling dynamics of marathons – A mixture model approach

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.