I'm trying to fit the distribution to the data. I started with histogram. Note that y axis is in logarithmic scale since the histogram is very steep. histogram
(source: mimuw.edu.pl)

How should proceed to find actual distribution. Should I modify my data first? Any guesses what could the actual distribution be?

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    $\begingroup$ Note that histograms are not great, in general, for assessing distributions. See this question. $\endgroup$ – ff524 Sep 4 '15 at 22:40
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    $\begingroup$ This is definitely a question for Cross Validated (CV). Actually, there are many answers to similar questions here, so it most likely will be declared a duplicate. To the OP: I suggest you to search CV for similar questions and answers. As a starting point, check references (especially, the first one) in my related CV answer. $\endgroup$ – Aleksandr Blekh Sep 4 '15 at 22:44
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    $\begingroup$ You cannot "proceed to find the actual distribution" from a sample. For any given distribution that might be a reasonable fit, there will be an infinite number of other distributions that are arbitrarily close to it. Distribution choice should be based on more than just the appearance of a histogram. Why do you need to identify a distribution? $\endgroup$ – Glen_b Sep 5 '15 at 2:58