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Records in athletics through extreme-value theory. (English) Zbl 1286.62047

Summary: We are interested in two questions on extremes relating to world records in athletics. The first question is: What is the ultimate world record in a specific athletic event (such as the 100-m race for men or the high jump for women), given today’s state of the art? Our second question is: How “good” is a current athletic world record? An answer to the second question also enables us to compare the quality of world records in different athletic events. We consider these questions for each of 28 events (14 for both men and women). {
} We approach the two questions with the probability theory of extreme values and the corresponding statistical techniques. The statistical model is of a nonparametric nature; only some “weak regularity” of the tail of the distribution function is assumed. We derive the limiting distribution of the estimated quality of a world record. {
} While almost all attempts to predict an ultimate world record are based on the development of world records over time, this is not our method. Instead, we use all top performances. Our estimated ultimate world record tells us what, in principle, is possible in the near future, given the present knowledge, material (shoes, suits, equipment), and drug laws.

MSC:

62G32 Statistics of extreme values; tail inference
62F07 Statistical ranking and selection procedures
62F10 Point estimation
62G05 Nonparametric estimation
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