Inequalities between the relational result sets cardinalities in random databases

In this study, we will analyze the cardinality of the ε-join random database operation for some representative types of attributes' probability distributions. The goal of our research is to establish and prove inequalities that take place between the cardinalities of the result sets obtained in these cases. In the beginning of our approach, we have focused on three representative continuous probability distributions: the uniform, the exponential and the normal, taking into consideration their standard forms. We will introduce the conclusions we could have drawn after the practical experiments which we have performed, we will state these results and we will provide a sound proof for them.