I have distributional data which I represent as a density. The data represents frequencies of user activities on a computer screen (e.g. amount of clicks on the y or x-axis of that screen but also other activities that can be related to coordinates and can therefore be binned by those coordinates (e.g. 5 pixels bins)). I would like to compare two kinds of that behavior and find out how compatible their distributions are. Very general. No assumptions exist. I can't assume parametric conditions such as linearity or normality.
I read about Lorenz curves and the Gini coefficient to be very much like what I need to compare distributions but also know that those methods find application primarily for economic and sociological problems and are usually not applied for general distributions. Am I applying the wrong tool for the job? What is your opinion about this? What alternatives do you recommend in order to find out how similar two distributions are?