overlap integrals for empirical data
I have two sets of data each originating from a different probability density function for a continuous stochastic variable (I do not know how these functions look like exactly). I am interested in the overlap integral of the two probability densities. I suppose the simplest way would be to bin the data and then consider probabilities for these bins. I wonder, however, whether there is a more sophisticated method... maybe something like considering overlap integrals between Gaussians that are centered on data points?