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How to split my data based on its fit within a Mixture Distribution?

Posted 10 years ago

Hi

I'm new to mathematica and would appreciate some help on what may be a simple problem (though I haven't been able to find any relevant methods). I have a dataset with two unknown distributions. For the simple case I'm assuming two Gaussian distributions but will expand once I get the base case working.

edist = EstimatedDistribution[data, MixtureDistribution[{p, 1 - p}, {NormalDistribution[a, b], 
    NormalDistribution[c, d]}]]

MixtureDistribution[{0.423334, 0.576666}, {NormalDistribution[1.34634, 0.46282], NormalDistribution[2.50805, 0.769406]}]

Which plots as the following:

enter image description here

I want to split my data into two separate data sets based on whether the data is contributing to distribution a or b. How would I go about this? I would have thought that data assigned to each distribution (after iterating through to optimise maximum likelihood) should be callable/extractable.

Thank-you in advance, Ivan

POSTED BY: Ivan Schroder
2 Replies

I agree with what Sean wrote. You can fit your data and find parameters for each distribution in that mixture distribution. You can then plot each of the distributions separately and find probabilities for any interval, but that's about where the data separation ends.

POSTED BY: Kay Herbert

If I am understanding your question, then the answer is that you can't do this. It doesn't make sense.

Suppose a random sample from the distribution edist has the value "2" in it. How are you supposed to know whether that 2 is a result of the first or second normal distribution? You can't.

You could calculate the probability that it came from either the first or the second normal distribution. Is that what you want to do? That problem can be solved by Baye's theorem.

POSTED BY: Sean Clarke
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