|University of Oslo
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In this thesis we analyze the performances of six different track and field disciplines (100m, 200m, 110m hurdles, 400m, 800m and 10000m) using mainly extreme value statistics. Besides fitting the generalized Pareto distribution to each of the disciplines (chapter 2), we also do a model selection (chapter 3) using AIC, BIC, TIC and FIC, with the latter being used to select a model for estimating the world record probability. Using the AIC we are able to reduce the total amount of parameters from twelve to seven, and with the FIC we find that we are able to use either the shape parameter of 100m or 800m on all six disciplines. We then take a step back in chapter 4 were we do an empirical Bayes analysis in an attempt to reduce the total mean square error of the shape parameter. We are successful with our method of moments approach, while the maximum likelihood approach fails. In chapter 5 we focus just on 100m as we add time as a covariate on the scale parameter. We also introduce the Poisson-GPD model, allowing us to model the probability of a new world record on a seasonal basis. At the end of the chapter we do a short analysis of Usain Bolt's performances using a regression model with N(0,1) distributed errors, as well as attempting a wind correction. In the last chapter (chapter 6) we summarize and discuss our findings.