Abstract:
In mathematical modelling problems relating to sports games, the running or swimming time of athletes is usually assumed to follow a normal distribution. This paper statistically and theoreti-cally analyzes the data collected from some real Marathon and Triathlon games, and shows that in a sports event the athletes’ average speed has a general normal distribution, whereas the time taken by the athletes arriving at a fixed point (e.g., the destination) in the race course does not follow such type of distribution, but rather a parameter-varying right-skewed normal-like distribution. Moreover, the mathematical formula for the probability density function of the athletes’ race time is derived, and the results obtained may also be applied to the corresponding mathematical modelling problems of similar sports games or other application areas.