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I have 240 samples and their relative frequencies (calculated from empirical observations), hence I have the probability distribution. It looks like this (hypothetical values):

Sample    Number Of Occurrences    Probability
----------------------------------------------
  1               19                 0.00001 = 19/sum(occurrences)
  2               1200               0.02
 ...              ...                ...
 240              345                0.0003

How can I determine which distribution (beta, exponential, ...) fits my data the best and with which parameters? Or, on a higher level, how can I inspect my distribution and draw interesting conclusions about other distributions? I mean, I can plot the probabilities of the samples, but what else?

I already came across this post but it doesn't really answer the question: Does my data come from a gamma or beta distribution?

I am working with R so any information with regard to that is also very helpful.

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GS9
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    Questions like this don't always (or often) have good answers, unfortunately. What are you actually looking for in the data? – shadowtalker May 05 '15 at 19:31
  • why do you want it to fit a parametric distribution? as to what else you might get from your data: first, plot it. second, everything you need to know about your distribution is described by its moments--mean, variance, skewness, kurtosis being the simplest central average based moments. but to know where to start, you need to answer @ssdecontrols question--what are you using the data for, and what would you like it to tell you? – MichaelChirico May 06 '15 at 05:05
  • Well, basically, I'd like to know what distribution my distribution is "most similar" to, although I don't know how "similarity" can be defined here. – GS9 May 06 '15 at 07:18
  • The problem is there's an infinite number of distributions that will be arbitrarily close to some given distribution. You have to narrow the problem space way down or settle for a somewhat different kind of question. – Glen_b May 06 '15 at 09:27

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