German tank problem

The problem is named after its use by Allied forces in World War II to estimate the monthly rate of German tank production from limited data. The approach enjoys the manufacturing practice of assigning and attaching ascending sequences of serial numbers to tank components, with some tanks being captured in battle by Allied forces. \(N\) being the total number of tanks produced, \(m\) being the highest serial number observed and \(k\) being the number of tanks captured, the estimator for \(N\) is given by:

\[ \hat{N}=m+\frac{m}{k}-1 \]

This simulation aims to demonstrate whether this is actually a good estimation method.