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I'm analyzing a set of data, and I like to fit a gamma distribution. I know how to do it in one dimension, but the data that I'm analyzing now are two dimensional. Is there any way that I can have a bivariate gamma function fitted into the data?

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You can find other versions of the bivariate gamma distribution in the following paper by Nadarajah:

http://www.emis.de/journals/HOA/MPE/2005/2151.pdf

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Yes, and there are several variants of the bivariate gamma distribution you can choose from. The VGAM package in R has one of them as a function. You can also use the Wishart distribution (which is a multivariate generalization of the gamma), or program your own bivariate gamma distribution. You'll probably want to use the optim function to find the MLE, although some hand-holding may be required.

A good general-purpose source for bivariate / multivariate Gamma distributions is Johnson, Balakrishnan, and Kotz, Continuous Multivariate Distributions.

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