I have two distributions which are derived from 2 separate sets of data. These distributions are not normal, and it is not clear at this point if they belong to any family of known pdfs (they are not symmetric either). Given a data point, I need to decide which distribution it is most likely to belong to. If these were normal distributions, I could do usual parametric tests and go from there, but in this case I am not sure how to proceed. I searched around a bit, but I couldn't find anything, probably because I am not using the right keywords. Any help is much appreciated.
Edit to clarify: I should have mentioned that it was univariate. I might as well explain the actual problem here as well. We have time-spent data for users on websites. We also have information on whether a user liked or disliked some of those sites (about 4% of all the sites). So we know the distribution of time spent for like and dislike. An obvious question, then, is for a random user who spent x amount of time, are they more likely to have liked the page or dislike the page. Our time spent information is based on seconds, so the distributions are really discreet, but in real life, they are continuous.