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Wiener process (brownian motion), normal distribution, log-normal, and mean-reversion are 4 most frequently used stochastic processes in modelling.

i wonder, given 30-50 sample points, is there a way/process to identify which of the 4 distributions best describe a random variable X(t)?

Even Wiener process might not be easy to distinguish as the sample points is not too many, -- we are not assuming X(t) must be one of the 4 processes, the target is just to find the best distribution to describe X(t).

It would be most preferred if there's some "industry de facto standard process" of such pattern recognition.

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The entire field of statistics is aimed at solving this problem. There are a huge number of ways to approach it. – Nate Eldredge Feb 27 at 2:13
@nate-eldredge sorry if i post a baby-stuff question. mind if give a couple of links? – athos Feb 27 at 2:21

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