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I have statistical variables whose values are real and follow gamma distributions. However, the distributions of each of those variables have a different mean and shape parameter.

I want to know what would be the distribution of a weighted mean of those variables.

I would as well need to know what would happen if the considered variables follow an other kind of distributions or if we I apply other operators (log, exp...)

Thereof, could someone suggest a reference book on this topic ? I had a look at the "Hand-book on Statistical Distributions" by C. Walck and though it is quite useful for their descriptions, it did not really help me there.

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My answer here contains a page with many of the common random variables and how they are related via various transformations. I'm not sure that's exactly what you're looking for, but perhaps it will help. –  Mike Spivey Jan 30 '13 at 23:30

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I've found Robert B. Ash's online Lectures on Statistics to be a well written overview of statistical techniques. In particular his first lecture (pdf) on transformations of random variables.

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