Functional Models and Probability Density Functions

There exist many approaches to discern a functional relationship between two variables. A functional model is useful for two reasons: Firstly, if the function is a relatively simple model in the plane, it provides us with qualitative information about the relationship. Secondly, given a fixed value for one variable, the other one can be calculated as a means for prediction. In this paper an approach for the extraction of functional models from probability density functions is proposed. The transformation of the conditional probability density function into a single value or a set of values is the basis for our discussion. Several transformations such as the mean value, the median and the modal intervals are well established. Regression models are compared to the functional models introduced here and as a consequence, two indicators to relate functional models to probability density functions are provided.