Bivariate Extreme Analysis of Olympic Swimming Data

Abstract

We model the times of the gold medalist swimmers in the Olympic Games. As the data represent an extreme value we use methods from extreme value theory. Features of the recorded variables lead to the inclusion of mixed parametric and nonparametric modeling for the marginal nonstationarity, constraints on marginal parameters to account for stochastic ordering between times from different events, and bivariate modeling to capture dependence across winning event times. Our analysis provides greater insight into the progression of winning times.

Keywords:

• 60G70
• 62E10
• 62G30
• 62G32
• 62P99

Keywords:

• Bivariate extreme value theory
• Generalized extreme value distribution
• Olympic Games
• Penalized likelihood
• Stochastic ordering

Acknowledgments

The first author was supported by a postgraduate grant (SLAB) from the Government of Malaysia and Universiti Putra Malaysia, Serdang. The work for this article was carried out at Lancaster University.