# How can i compute the probability that a cloud of points was created by a probability distribution?

I have a number of probability distributions that describe a number of points. like this:

Now if i have draw a one point out of each distribution, i get a bunch of points randomly set on the 2-dimensional surface. How can i, given the set of probability distributions and a set of points compute the probability that i would draw something like that again? What is the correct mathematical term for what i want to compute?

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– Did Jul 19 '12 at 16:26

## 1 Answer

If I understand your question right, then what you want is to develop a statistical test.

Essentially, given some sampling of points $P = \left\{ p_1, p_2,\ldots,p_n\right\}$, you need to estimate the probability that this sampling of points resulted from some distribution. In this case, your null hypothesis is that $P$ was drawn from your presumed distribution. You will want to set a threshold for statistical significance. In other words, there is no concrete, deterministic way to distinguish between a set of points happening to randomly align with your chosen distribution by sheer luck, or whether they actually came from your distribution.

There are many such tests; a basic example is a chi-squared test. Off-hand, I don't know which test is best for your application, but the Wikipedia page should direct you to some good information.

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