Modern railway signal systems allow the collection of very large data sets (more than a thousand values). These data sets are often rounded by the signal technology, so that the values are effectively discrete. This paper reviews other literature on fitting distributions to large data sets, and then shares the experience of distribution fitting to a large data set from the Danish railways.Modern railway signal systems allow the collection of very large data sets (more than a thousand values). These data sets are often rounded by the signal technology, so that the values are effectively discrete. This paper reviews other literature on fitting distributions to large data sets, and then shares the experience of distribution fitting to a large data set from the Danish railways