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Ordinal regression falls between discrete-valued classification andcontinuous-valued regression. Ordinal target variables can be associated withranked random variables. These random variables are known as order statisticsand they are closely related to ordinal regression. However, the challenge ofusing order statistics for ordinal regression prediction is finding a suitableparent distribution. In this work, we provide a case study of a real-worldorienteering relay race by viewing it as a random process. For this process, weshow that accurate order statistical ordinal regression predictions of finalteam rankings, or places, can be obtained by assuming a lognormal distributionof individual leg times. Moreover, we apply Fenton-Wilkinson approximations tointermediate changeover times alongside an estimator for the total number ofteams as in the notorious German tank problem. The purpose of this work is, inpart, to spark interest in studying the applicability of order statistics inordinal regression problems.

Fenton-Wilkinson Order Statistics and German Tanks: A Case Study of an Orienteering Relay Race