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

Baker, RD

Abstract

In 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 2 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 2 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, that exploits the fact that the integral to be
evaluated is an iterated integral.

Citation

Baker, R. (2020). New order-statistics-based ranking models and faster computation of outcome probabilities. IMA Journal of Management Mathematics, 31(1), 33-48. https://doi.org/10.1093/imaman/dpz001

• Journal Article Type: Article
• Acceptance Date: Jan 14, 2019
• Online Publication Date: Feb 8, 2019
• Publication Date: Jan 1, 2020
• Deposit Date: Jan 17, 2019
• Publicly Available Date: Feb 8, 2020
• Journal: IMA Journal of Management Mathematics
• Print ISSN: 1471-678X
• Electronic ISSN: 1471-6798
• Publisher: Oxford University Press
• Volume: 31
• Issue: 1
• Pages: 33-48
• DOI: https://doi.org/10.1093/imaman/dpz001
• Publisher URL: https://doi.org/10.1093/imaman/dpz001
• Related Public URLs: https://academic.oup.com/imaman