What methods exist to measure how similar a set of sampled distributions are to each other? I have a set of distributions that are sampled. How do I measure their similarity between themselves or as a group/set?
So, given a finite domain for a sampled function$F_j(x)$, with $x_i \in {1,\ldots,N}$ and $j \in {1, \ldots, J}$. I would like a measure $\cdot(F_{1,J})$ for how similar the distributions are, or test of whether whether they are statistically close enough, eg. a test producing some p-value. 
 A: 
I have a set of distributions that are sampled.

From your question, I don't quite know what you are trying to achieve. 
You have theoretical distributions $F_{1:J}$, and you sampled N datapoints from each, giving you J samples of size N.


*

*Are you trying to identify which sample was created by which
theoretical distribution? 


In that case one approach would be to calculate the
   Kulback-Leibler divergence between the theoretical distributions
   $F_1, \ldots, F_J$ for the empirical distribution of the given
   sample.


*

*Are you trying to identify how similar are the samples to
each other? 


In that case you would want to calculate the divergence
   between their empirical distributions. You might want to check out the following talk on calculating KL of empirical distributions:
http://videolectures.net/ripd07_cruz_kld/
If you are a fan of p-values, there is an entire set of goodness-of-fit tests for samples and theoretical distributions.
http://en.wikipedia.org/wiki/Goodness_of_fit
Please be aware that unlike men, not all statistical tests are created equal...
HTH!
