Dear All,   
      
   I have an interesting problem here. I am not sure if I have posted   
   this question before, but have had no responses so far and so trying   
   again.   
      
      
   My problem is related to markov models.   
      
      
   My scenario is:   
      
      
   1) I have an observation matrix of million events N...this is usually   
   inter arrival times of packets of particular protocols in random   
   networks, so depending on the protocols they will have some   
   distributions.   
      
      
   2) If i plot N+1 over N and then use 3d Histogram or density plots   
   for   
   the million events, this will allow me to see the distributions   
   shapes, whether poisson, gaussian or continous random distributions.   
   Irrespective of the distributions, I can shrink the number of bins   
   blindly and using the counts density of each bin [nXn], I can   
   normalise the values across the columns and build the state   
   transition   
   matrix, and hence I have a Markov model with states which are related   
   to the number of bins I shrink down to. But doing this will give me   
   only a very basic fit of the model.   
      
      
   3) To get a better model with optimum fit, I need to replace the   
   distributions I find in the graphs, with relevant appropriate state   
   transitions.....and this is where my problem is. I have not been able   
   to understand how to replace these distributions with unique state   
   transitions.   
      
      
   Anybody who can help me in this, I will be really grateful. If you   
   have not understood my problem, I am willing to clarify further.....   
      
      
   But in general, I need help with a mathematical relationship between   
   a   
   distribution in an observation matrix and an appropriate state   
   transition.   
      
      
   Many thanks in advance,   
      
      
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