How to create an unbiased fit to the data (Keyboard log data for each user)

Hi all ,

So I have a very simple distribution of events (eg user keyboard log for five employees).
Now if suppose I consider frequency of each key pressed for a single user, and for all users.
And then suppose I want to see what distribution this data follows ( without any bias toward any type of distribution, i.e. i want to get unsupervised insight from this distribution, rather than trying to fit it into something with a bias).
Also what higher order statistics can I generate from this simple keyboard log data ?
what about multivariate

what do you mean by "higher order statistics" here?
Thanks Ted,

By higher order I meant things besides the usual "mean,median,variance....".
For example if Im given a data, and I plot it. Then I want to fit this distribution. But I would not like to have any bias towards any "particular distribution", to fit on this data. So is there any method through which I can know without any bias -
"The distribution of the data".
In this case I think the estimated multivariate distribution is just the empirical distribution. I don't know what other distributions you're thinking of for these keystroke data. If you mean higher order moments I suppose you could look at things like sample kurtosis etc., but I don't know what they would mean here.