**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**31107

##### Ordinal Regression with Fenton-Wilkinson Order Statistics: A Case Study of an Orienteering Race

**Authors:**
Joonas Pääkkönen

**Abstract:**

**Keywords:**
Sports Analytics,
Orienteering,
order statistics,
log-normal distribution,
ordinal regression,
Fenton-Wilkinson approximation,
sports modeling,
German tank
problem

**References:**

[1] P. A. Gutierrez, M. Perez-Ortiz, J. Sanchez-Monedero, F. Fernandez-Navarro, and C. Hervas-Martinez, “Ordinal regression methods: Survey and experimental study,” IEEE Trans. Knowl. and Data Eng., vol. 28, no. 1, pp. 127–146, 2016.

[2] M. Raghu and E. Schmidt. (2020, March) A survey of deep learning for scientific discovery.

[Online]. Available: arXiv:2003.11755

[3] M. Strand and D. Boes, “Modeling road racing times of competitive recreational runners using extreme value theory,” Am. Stat., vol. 52, no. 3, pp. 205–210, 1998.

[4] H. Spearing, J. A. Tawn, D. B. Irons, T. Paulden, and G. A. Bennett. (2020, June) Ranking, and other properties, of elite swimmers using extreme value theory.

[Online]. Available: arXiv:1910.10070

[5] L. F. Fenton, “The sum of log-normal probability distibutions in scattered transmission systems,” IRE Trans. Commun. Syst., vol. 8, pp. 57–67, 1960.

[6] R. I. Wilkinson, “Unpublished, cited in 1967,” Bell Telephone Labs, 1934.

[7] B. R. Cobb, R. Rum´ı, and A. Salmer´on, “Approximating the distribution of a sum of log-normal random variables,” in Proc. 6th Eur. Workshop Probab. Graph. Models, 2012, pp. 67–74.

[8] S. Nadarajah, “Explicit expressions for moments of log normal order statistics,” Economic Quality Control, vol. 23, no. 2, pp. 267–279, 2008.

[9] E. T. Jaynes, “Information theory and statistical mechanics,” Phys. Rev., vol. 106, no. 4, pp. 620–630, 1957.

[10] E. J. Allen, P. M. Dechow, D. G. Pope, and G. Wu, “Reference-dependent preferences: Evidence from marathon runners,” Manag. Sci., vol. 63, no. 6, pp. 1657–2048, 2017.

[11] D. Ruiz-Mayo, E. Pulido, and G. Mart´ı˜noz, “Marathon performance prediction of amateur runners based on training session data,” in Proc. Mach. Learn. and Data Min. for Sports Anal., 2016.

[12] J. Esteve-Lanao, S. D. Rosso, E. Larumbe-Zabala, C. Cardona, A. Alcocer-Gamboa, and D. A. Boullosa, “Predicting recreational runners’ marathon performance time during their training preparation,” J. Strength Cond. Res. doi: 10.1519/JSC.0000000000003199

[Epub ahead of print], 2019.

[13] K. A. Wang, G. Pleiss, J. R. Gardner, S. Tyree, K. Q. Weinberger, and A. G. Wilson, “Exact gaussian processes on a million data points,” in Proc. Adv. Neural Inf. Process. Syst. 32, 2019, pp. 14 648–14 659.

[14] C. E. Rasmussen and C. K. I. Williams, “Gaussian processes for machine learning,” The MIT Press, 2006.

[15] Gpytorch regression tutorial.

[Online]. Available: https://gpytorch.readthedocs.io/en/latest/examples/01 Exact GPs/ Simple GP Regression.html

[16] Mord: Ordinal regression in python.

[Online]. Available: https: //pythonhosted.org/mord/

[17] F. Pedregosa-Izquierdo, “Feature extraction and supervised learning on fmri: from practice to theory,” Ph.D. dissertation, Universit´e Pierre-et-Marie-Curie, 2015.

[18] Jukola 2019.

[Online]. Available: https://results.jukola.com/tulokset/en/ j2019 ju/

[19] E. Limpert, W. A. Stahel, and M. Abbt, “Log-normal distributions across the sciences: Keys and clues,” Bioscience, vol. 51, pp. 341–352, 2001.

[20] P. Chen, R. Tong, G. Lu, and Y. Wang, “Exploring travel time distribution and variability patterns using probe vehicle data: Case study in beijing,” J. Adv. Transp., pp. 1–13, 2018.

[21] R. Ruggles and H. Brodie, “An empirical approach to economic intelligence in world war ii,” J. Am. Stat. Assoc., vol. 42, no. 237, pp. 72–91, 1947.

[22] L. A. Goodman, “Serial number analysis,” J. Am. Stat. Assoc., vol. 47, no. 270, pp. 622–634, 1952.