Understanding the distribution of crime victimization using ‘British crime survey’ data: an exercise in statistical reasoning

This paper focuses upon the question of understanding the data generating process that gives rise to the frequency distribution of crime victimization count data sampled from the British Crime Survey (BCS). Having described the form of this data, the paper introduces the problem of explaining the over-dispersion of the distribution. It discusses and compares various models of the data that make assumptions about the data generation process, including risk-heterogeneity, state-dependency, conditional probability, the double hurdle model, and the spells model. Its principal conclusion is that the crime victimization frequency distribution found in BCS data is the heterogeneous product of the mixing of two probability distributions: one concerns victim-prevalence, where zero-inflation predominates; the other concerns victimization-frequency, expressing the long-tail of high-frequencies. This conceptualization sheds new light on some persistent difficulties that might point the way towards future progress in understanding and remedying the distribution of crime victimization amongst citizens