@article{(Open Science Index):https://publications.waset.org/pdf/10011308,
	  title     = {Ordinal Regression with Fenton-Wilkinson Order Statistics: A Case Study of an Orienteering Race},
	  author    = {Joonas Pääkkönen},
	  country	= {},
	  institution	= {},
	  abstract     = {In sports, individuals and teams are typically interested
in final rankings. Final results, such as times or distances, dictate
these rankings, also known as places. Places can be further associated
with ordered random variables, commonly referred to as order
statistics. In this work, we introduce a simple, yet accurate order
statistical ordinal regression function that predicts relay race places
with changeover-times. We call this function the Fenton-Wilkinson
Order Statistics model. This model is built on the following educated
assumption: individual leg-times follow log-normal distributions.
Moreover, our key idea is to utilize Fenton-Wilkinson approximations
of changeover-times alongside an estimator for the total number
of teams as in the notorious German tank problem. This original
place regression function is sigmoidal and thus correctly predicts
the existence of a small number of elite teams that significantly
outperform the rest of the teams. Our model also describes how place
increases linearly with changeover-time at the inflection point of the
log-normal distribution function. With real-world data from Jukola
2019, a massive orienteering relay race, the model is shown to be
highly accurate even when the size of the training set is only 5%
of the whole data set. Numerical results also show that our model
exhibits smaller place prediction root-mean-square-errors than linear
regression, mord regression and Gaussian process regression.},
	    journal   = {International Journal of Computer and Information Engineering},
	  volume    = {14},
	  number    = {7},
	  year      = {2020},
	  pages     = {242 - 247},
	  ee        = {https://publications.waset.org/pdf/10011308},
	  url   	= {https://publications.waset.org/vol/163},
	  bibsource = {https://publications.waset.org/},
	  issn  	= {eISSN: 1307-6892},
	  publisher = {World Academy of Science, Engineering and Technology},
	  index 	= {Open Science Index 163, 2020},
	}