Difference equation models for estimating athletic records

This article presents an analysis of the models that are frequently used for estimating the future records for atheletic events. It considers an innovative approach for modeling based on difference equations whose complementary solution yields one of these models. It does this by establishing a relationship between the models and certain difference equations. Moreover, it shows that each of those models can be converted to the exponential model by applying an appropriate substitution. Based on the derived relations it proposes a numerical procedure for estimating the model parameters and discusses its advantages over an existing procedure. This procedure reduces the computational cost and avoids the classical difficulties of non-linear optimization procedures such as the Newtonʹs method. Finally, it tests the proposed numerical procedure using simulated data and applies the procedure to the fastest times for 400 m race.