The question in short: What methods can be used to quantify distributional relationships between data when the distribution is un-known?
Now the longer story: I have a list of distributions and would like to rank them based on their similarity to a given base-line distribution. Correlation jumps into my mind in such a case and the Spearman correlation coefficient in particular given that it does not make any distributional assumptions. However, I would actually need to create the coefficient based on binned data (as this is done for histograms or densities) rather than the raw data and I don't know if this is actually a valid step or if I am just manufacturing data.
In other words, if I have a 10000 point data set for each distribution, I would first create a binned distribution for each were each bin is of equal width and contains the frequencies of how many points each bin has. Just the way this is done for density plots or histograms. Each bin is on a discrete scale. The data is actually computer screen coordinate data and values are between 1 and 1024. Each pixel position could represent a bin (but larger bins are possible e.g. every 5 pixel being one bin). I would then compare the sequence of bins with each other rather than the raw data. The data set would look like this.
bins: 1 2 3 4 .... 1024
dist#base:1 2 2 3 ..... 3
dist#1: 1 4 5 5 3
dist#2: 2 2 3 5 6
dist#1000: 1 2 4 6 6
Does this make sense? Are there better ways of doing that? Are there better statistical methods? The goal of all this is to first) test how close are distributions from measure A to measure B and second) if I can predict one, if the other is missing.