Men's Performance in Triple Jump: an approach with Extreme Value Theory

Abstract

Emil Gumbel was the first to use extreme value models in statistics applications. In the block method an Extreme Value distribution is fitted to the sample of block maxima obtained from non-overlapping blocks of a series of random variables. The block length is usually long (usually chosen as one year), to assure the independence of the block maxima sample. Although this method has proved to be useful in diversified situations, it has also been criticized since we are wasting information by using only the observed maxima from each block. To use more information about the tail of the model underlying the data, the block maxima method was more recently extended to the r−largest order statistics method. The choice of the number r ≥ 1 of largest order statistics taken from each block must be made with careful, due to the usual bias and variance trade-off. In this work we use the r−largest order statistical method to study the limit of men’s performance in Triple Jump event. Our results indicate a negative extreme value index and thus a finite right endpoint for the extreme value model.