On the Statistical Distribution of Object-Oriented System Properties

Abstract—The statistical distributions of different software properties have been thoroughly studied in the past, including software size, complexity and the number of defects. In the case of object-oriented systems, these distributions have been found to obey a power law, a common statistical distribution also found in many other fields. However, we have found that for some statistical properties, the behavior does not entirely follow a power law, but a mixture between a lognormal and a power law distribution. Our study is based on the Qualitas Corpus, a large compendium of diverse Java-based software projects. We have measured the Chidamber and Kemerer metrics suite for every file of every Java project in the corpus. Our results show that the range of high values for the different metrics follows a power law distribution, whereas the rest of the range follows a lognormal distribution. This is a pattern typical of so-called double Pareto distributions, also found in empirical studies for other software properties. Keywords-object-oriented properties; statistical distribution; Chidamber & Kememer; double Pareto; lognormal; power law