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Let's say I have many measures of a random variable - x. Moreover, I have many measures of y and z. Meaning I can approximate their PDF by the histogram of the measures.

How can I estimate the joint PDF of (x, y, z)? I don't know whether they are uncorrelated.

Thanks.

P.S. References to a practical demos and info on the subject are welcome.

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    pdf are for continuous. I think you are looking at a discrete problem.2011-03-03

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If you have measurements of $x$, $y$ and $z$ isolated, you can estimate the density functions (histograms, or whatever) of each one.. isolated. That is (assumming $x$, $y$ and $z$ are random variables that have a join density, i.e. that each ocurrence corresponds to a tuple $(x,y,z)$), you can estimate the marginal densities. And nothing more. The joint density is the product of the marginals if (and only if) the variables are independent. If you cannot assume that, and if you dont have more data, you can't estimate the joint density.

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    @TimSwast: then you'd probably use some parametric estimation; for example, you'd assume that the variables are jointly gaussian, and you'd estimate te unknown parameters from the data. Of course, you'd need some basis for that assumption.2012-09-04