New order-statistics-based ranking models and faster computation of outcome probabilities

Abstract

AbstractIn sport, order-statistics-based models such as Henery’s gamma model and the Thurstone–Mosteller type V model are useful in estimating competitor strengths from observed performance of players in competitions between two or more players. They can also be applied in many other areas, such as analysis of consumer preference data, which would be useful to marketing management. Two new families of such models derived from the exponentiated exponential, and Pareto distributions are introduced. Use of order-statistics-based models when there are more than two competitors has been hampered by lack of an efficient method of computation of outcome probabilities as a function of competitor strengths, and a fast method of computation of outcome probabilities is presented, which exploits the fact that the integral to be evaluated is an iterated integral.