Prevention rates were obtained based on complementary homici

Prevention rates were obtained based on complementary homicide rates, other thefts and vehicle theft rates weighted by the population. If we consider , as the highest homicide rate among the Federation units in a nevertheless t and as the homicide rate standard deviation, then the homicide prevention rate for unit i, in a period t, is given by;where is the homicide rate for the Federation unit i, in a period t and N is the relation between the unit i population and the population of the unit with the highest homicide rate. The other prevention rates follow the same formula. On Table 1, the state averages for these variables related to the years 2008 and 2012 are introduced. In the Homicides, Vehicles and Thefts columns, you will find statistics related to the average number of homicides, car thefts and other thefts per 100,000 people. The column expenses introduces information related to the per capita expenses with public security, except for police-related expenses. The columns Military and Civil correspond to the number of military and civil policemen per 1000 people.
Analysis of results According to Krüger (2012), when there are no outliers present or there are measurement errors in the data sampling, the DEA and FDH methods are more suitable than the order—m frontier. In this sense, the Super efficiency test was firstly carried out based on the Andersen and Petersen (1993) models to verify the possible presence of outliers in the sample. Table A1 in the article Appendix shows the super efficiency scores and the corrected z statistics. Super efficiency results tests suggest the existence of outliers: Alagoas, in 2009; São Paulo, in 2010; Paraná, in 2009, 2010, 2011 and 2012. Once the presence of outliers in the sample is identified, there are two possible procedures: (a) eliminating them from the sample and proceeding to estimate inefficiencies using the DEA or FDH models or (b) keeping the original sample and outlier-robust estimation methods. We chose the second alternative and efficiencies were estimated using the order—m frontier method. According to Cazals et al. (2002), the lower the m value in relation to the sample size, the more robust the order—m estimator becomes for extreme values and outliers. On the other hand, the estimated frontier gets further away from the real frontier. It is up to the researcher to adjust the m values according to his goals. In mammal-like reptiles study, we used several m values that could make order—m efficiency scores quite different from the scores obtained through FDH. The m value was equal to 20. Table 2 values show the annual mean values and the public security efficiency order, as well as the Homicide, Vehicle Theft and Other Thefts rates in Brazilian states.
Final considerations