We introduce here an index, which we call the Rare Event Concentration Coefficient (RECC), that is a measure of the dispersion/concentration of events which have a low frequency but tend to have a high level of concentration, such as the number of crimes suffered by a person. The Rare Event Concentration Coefficient is a metric based on a statistical mixture model, with a value closer to zero meaning that events are homogeneously distributed, and a value closer to one meaning that the events have a higher degree of concentration. This measure may be used to compare the concentration of events over different time periods and over different regions. Other traditional approaches for the dispersion/concentration of a variable tend to be blind to structural changes in the pattern of occurrence of rare events. The RECC overcomes this issue and we show here two simple applications, first by using the number of burglaries suffered in Netherlands and then by using the number of volcanic eruptions in the world.