What I would like to do is create a tool that takes as an input, a set of samples that are known to behave according to a known probability distribution and predict the next sample. The tool will evaluate n samples and predict the n+1 sample. I want to compare the predicted sample to the actual sample. I would like to be able to change the assumptions about the data by choosing different probability distributions. The purpose of the tool is to identify samples that don't fit the assumption of the chosen probability distribution.
closed as not a real question by Yves Klett, whuber, rcollyer, rm -rf♦ Dec 31 '12 at 18:53
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Here is a worked example:
We take as our data 10000 samples from a Normal Distribution with mean 1 and standard deviation 3:
We then try to work backwards to see what the data says about the distribution - taking as an assumption that it came from a Normal Distribution, we see which paramaters are most consistent with the data:
We could of course have tried to fit other distributions to the data:
Once we have estimated parameters for our sample distribution we can then simulate further points using