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I have a number of distance matrices that I want to associate their members with a probability distribution. Is there a method which can affiliate each distance matrix with a distribution?

EDIT: Lets say I have a distance matrix like:

     A1    A2    A3    A4   ...
A1   X     1     3     2
A2   1     X     4     3
A3   3     4     X     3
A4   2     3     3     X
 .
 .
 .

Now I want to see what are the distribution parameters if members of this matrix were from a probability distribution. I only have the matrix and I do not know what is the distribution of the data.

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  • $\begingroup$ Do want to (a) estimate a probability distribution for the set of matrices, (b) estimate a probability distribution for the individuals giving rise to any individual matrix, or (c) something else? Please clarify. $\endgroup$
    – whuber ♦
    Commented Jan 16, 2014 at 23:26
  • $\begingroup$ @whuber I put more info in the question. Here I mean (b). $\endgroup$
    – POD
    Commented Jan 16, 2014 at 23:34
  • $\begingroup$ In order to get a useful answer, I believe you will need to supply more context and assumptions. After all, we don't even know what kind of similarity you are calculating nor anything about the possible statistical distribution of the objects. $\endgroup$
    – whuber ♦
    Commented Jan 16, 2014 at 23:42
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    $\begingroup$ @whuber I am trying to find a distribution for a set of sequences (each sequence has a different length but finite). I am using edit distance to calculate the distance between each sequence and put it in a matrix. Now I want to see how can I find a distribution that explains the distance between sequences. $\endgroup$
    – POD
    Commented Jan 16, 2014 at 23:50

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