| Low probability count data are often encountered in routine activities in which a particular outcome is diverse and infrequent. Crime is such an activity in that the probability of occurrence at a particular place or time is close to zero. Low probability count data are analyzed in this research with crime data used to illustrate applications of the techniques developed. Crime was chosen for this research because it has become a measure for quality of life and the public is increasingly concerned with reducing and controlling criminal activity.;This work focuses on analytical techniques which are useful for low probability count data such as crime. The range of topics is diverse and includes three major topics. The first topic includes possible distributions of crime data along with a general description of the data and collection procedures. A Poisson-Binomial model is introduced which is then modified using Bayesian priors. All models are interpreted in terms of crime data and fit to crime counts for Waco, Texas. Two goodness-of-fit tests are reviewed and used to test the fit of each marginal distribution to the observed data.;The second topic reviews nonparametric statistics used to test for significant differences in the location of two populations. The Moore-Seaman statistic, introduced by Moore (1974), is compared to the Mann-Whitney U and t statistics. It is shown that the Moore-Seaman and Mann-Whitney U statistics produce equivalent test results. A criterion for construction of a most powerful nonparametric statistic is developed and it is shown that the Moore-Seaman and Mann-Whitney U statistics conform to this criterion. Finally, performance of the Moore-Seaman and Mann-Whitney U tests is compared to performance of the Median test and t-test.;The third topic introduces the use of process control techniques to crime analysis. After general introduction of the specific application, the data is reintroduced to stress the characteristics that imply this analysis technique is appropriate. Control chart theory is reviewed and interpreted in the context of crime data. |
