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During World War II, production of German tanks such as the Panther was accurately estimated by Allied intelligence using statistical methods
In the statistical theory of estimation, the German tank problem consists of estimating the maximum of a discrete uniform distribution from sampling without replacement. In simple terms, suppose there exists an unknown number of items which are sequentially numbered from 1 to N. A random sample of these items is taken and their sequence numbers observed; the problem is to estimate N from these observed numbers.
The frequentist prediction example:
Assuming tanks are assigned sequential serial numbers starting with 1, suppose that four tanks are captured and that they have the serial numbers: 19, 40, 42 and 60.
Let N equal the total number of tanks predicted to have been produced, m equal the highest serial number observed and k equal the number of tanks captured.
N = m + m/k - 1 = 74