Generally speaking, crime is, fortunately, a rare event. As far as modelling is concerned, this sparsity of data means that traditional measures to quantify concentration are not appropriate when applied to crime suffered by a population. Our objective is to develop a new technique to measure the concentration of crime which takes into account its low frequency of occurrence and its high degree of concentration in such a way that this measure is comparable over time and over different populations.
This article derives an estimate of the distribution of crime suffered by a population based on a mixture model and then evaluates a new and standardised measurement of the concentration of the rates of suffering a crime based on that distribution.
The new measure is successfully applied to the incidence of robbery of a person in Mexico and is able to correctly quantify the concentration crime in such a way that is comparable between different regions and can be tracked over different time periods.
The risk of suffering a crime is not uniformly distributed across a population. There are certain groups which are statistically immune to suffering crime but there are also groups which suffer chronic victimisation. This measure improves our understanding of how patterns of crime can be quantified allowing us to determine if a prevention policy results in a crime reduction rather than target displacement. The method may have applications beyond crime science.