Causal statistical modeling and calculation of distribution functions of classification features

Abstract: Statistical system models provide the basis for the examination of various sorts of distributions. Classification distributions are a very common and versatile form of statistics in e.g. real economic, social, and IT systems. The statistical distributions of classification features can be applied in determining the a priori probabilities in Bayesian networks. We investigate a statistical model of classification distributions based on finding the critical point of a specialized form of entropy. A distribution function for classification features is derived, with the two parameters $n_0$, minimal class, and $\bar{N}$, average number of classes. Efficient algorithms for the computation of the class probabilities and the approximation of real frequency distributions are developed and applied to examples from different domains. The method is compared to established distributions like Zipf's law. The majority of examples can be approximated with a sufficient quality ($3-5\%$).