Extreme value theory provides methods to analyze the most extreme parts of data. We predicted the ultimate 100 m dash records for men and women for specific periods using the generalized extreme value (GEV) distribution. The various diagnostic plots, which assessed the accuracy of the GEV model, were well fitted to the 100 m records in the world and Japan, validating the model. The men’s world record had a shape parameter of -0.250 with a 95% confidence interval of [-0.391, -0.109]. The 100 m record had a finite limit and a calculated upper limit was 9.46 s. The return level estimates for the men’s world record were 9.74, 9.62, and 9.58 s with a 95% confidence interval of [9.69, 9.79], [9.54, 9.69], and [9.48, 9.67] for 10-, 100- and 350-year return periods, respectively. In one year, the probability of occurrence for a new world record of men, 9.58 s (Usain Bolt), was 1/350, while that for women, 10.49 s (Florence Griffith-Joyner), was about 1/100, confirming it was more difficult for men to break records than women.
References
[1]
Coles, S. (2001) An Introduction to Statistical Modeling of Extreme Values. Springer-Verlag. https://doi.org/10.1007/978-1-4471-3675-0
[2]
Katz, R.W., Parlange, M.B. and Naveau, P. (2002) Statistics of Extremes in Hydrology. Advances in Water Resources, 25, 1287-1304. https://doi.org/10.1016/S0309-1708(02)00056-8
[3]
Embrechts, P., Klüppelberg, C. and Mikosch, T. (1997) Modeling Extremal Events for Insurance and Finance. Springer-Verlag. https://doi.org/10.1007/978-3-642-33483-2
[4]
Gilli, M. and këllezi, E. (2006) An Application of Extreme Value Theory for Measuring Financial Risk. Computationnal Economics, 27, 207-228. https://doi.org/10.1007/s10614-006-9025-7
[5]
Dawson, T.H. (2000) Maximum Wave Crests in Heavy Seas. Journal of Offshore Mechanics and Arctic Engineering-Transactions of the AMSE, 122, 222-224. https://doi.org/10.1115/1.1287039
[6]
Roberts, S.J. (2000) Extreme Value Statistics for Novelty Detection in Biomedical Data Processing. IEE Proceedings—Science Measurement and Technology, 147, 363-367. https://doi.org/10.1049/ip-smt:20000841
[7]
Lavenda, B.H. and Cipollone, E. (2000) Extreme Value Statistics and Thermodynamics of Earthquakes: Aftershock Sequences. Annali di Geofisica, 43, 967-982.
[8]
Maruyama, F. (2020) Analyzing the Annual Maximum Magnitude of Earthquakes in Japan by Extreme Value Theory. Open Journal of Applied Sciences, 10, 817-824. https://doi.org/10.4236/ojapps.2020.1012057
[9]
Brown, S.J. (2018) The Drivers of Variability in UK Extreme Rainfall. International Journal of Climatology, 38, e119-e130. https://doi.org/10.1002/joc.5356
[10]
Kawas, M.L. and Moreira, R.G. (2001) Characterization of Product Quality Attributes of Tortilla Chips during the Frying Process. Journal of Food Engineering, 47, 97-107. https://doi.org/10.1016/S0260-8774(00)00104-7
[11]
Thomas, M., Lemaitre, M., Wilson, M. L., Vibound, C., Yordanov, Y., Wackernagel, H. and Carrat, F. (2016) Applications of Extreme Value Theory in Public Health. PLoS ONE, 11, e0159312. https://doi.org/10.1371/journal.pone.0159312
[12]
Einmahl, J.H.J. and Magnus, J.R. (2008) Records in Athletics through Extreme-Value Theory. Journal of the American Statistical Association, 103, 1382-1391. https://doi.org/10.1198/016214508000000698
[13]
Einmahl, J.H.J. and Smeets, S.G.W.R. (2011) Ultimate 100-m World Records through Extreme-Value Theory. Statistical Neerlandica, 65, 32-42. https://doi.org/10.1111/j.1467-9574.2010.00470.x
[14]
Ito, H. and Okano, S. (2005) Analysis of Changes in the 100 m Records in Japan and the World. Bulletin of Athletics Research, 1, 61-66.
