[joe_the_user]

The question "what probability distribution generated this" is very hard to answer if you're only getting short window before the distribution changes. A lot of distributions could generate relatively "short" set dispersed data points and deciding which distribution is "really" creating the points might not even be meaningful. A distribution is a mathematical device, not something with a physical existence.

[mjburgess]

Probability distributions don't generate data, they describe our uncertainty about its generation retrospectively. So there is no answer to that question. The lack of such an answer is at the heart of why such inference is hard: in most cases, there isnt a stable underlying reality of anything doing the distributing.

[joe_the_user]

I think we're saying roughly the same thing. It's natural starting with a statistical model to say it generates data (as the article sometimes does) but in reality, you often/generated have data generated by a possibly deterministic and completely different process but satisfying (if you're lucky) the statistical conditions. Even in testing random/stochastic models, you would usually use pseudo-random generators - which are deterministic.