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.
[1]
J. Tawn,et al.
Extremal analysis of short series with outliers: sea‐levels and athletics records
,
1999
.
[2]
L. de Haan,et al.
On the maximal life span of humans.
,
1994,
Mathematical population studies.
[3]
Laurens de Haan,et al.
Approximations to the tail empirical distribution function with application to testing extreme value conditions
,
2006
.
[4]
L. de Haan,et al.
On the estimation of the exceedance probability of a high level
,
1990
.
[5]
Richard L. Smith.
Estimating tails of probability distributions
,
1987
.
[6]
L. Haan.
Estimation of the Minimum of a Function Using Order Statistics
,
1980
.
[7]
L. Haan,et al.
A moment estimator for the index of an extreme-value distribution
,
1989
.
[8]
Deyuan Li,et al.
On testing extreme value conditions
,
2006
.
[9]
Richard L. Smith.
Forecasting Records by Maximum Likelihood
,
1988
.
[10]
L. Haan,et al.
Extreme value theory : an introduction
,
2006
.
[11]
Jonathan A. Tawn,et al.
Statistics for Exceptional Athletics Records
,
1995
.
[12]
L. Haan,et al.
On optimising the estimation of high quantiles of a probability distribution
,
2003
.