Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In the statistical theory of estimation, estimating the maximum of a uniform distribution is a common illustration of differences between estimation methods. The specific case of sampling without replacement from a discrete uniform distribution is known, in the English-speaking world, as the German tank problem, due to its application in World War II to the estimation of the number of German tanks. Estimating the population maximum based on a single sample raises philosophical points about evaluation of estimators and likelihood (particularly bias in maximum likelihood estimators) and yields divergent results, depending on approach, while the estimation based on multiple samples is used in elementary statistics education as an instructive practical estimation question whose answer is simple but not obvious.

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