lorenzgini: generalized Gini for sparse data situations


lorenzgini is an R package that calculcates the standard Gini coefficient as well as the generalized coefficient, and plots Lorenz curves. The Lorenz plots show the line of maximal equality given the data. The package builds on this paper in which Wim Bernasco and I wrote that the crime and place literature lacks a standard methodology for measuring and reporting crime concentration. We suggested that crime concentration be reported with the Lorenz curve and summarized with the Gini coefficient, and we proposed generalized versions of the Lorenz curve and the Gini coefficient to correct for bias when crime data are sparse (i.e., fewer crimes than places). The proposed generalizations are based on the principle that the observed crime concentration should not be compared with perfect equality, but with maximal equality given the data. The generalizations asymptotically approach the original Lorenz curve and the original Gini coefficient as the number of crimes approaches the number of spatial units.