Transformation of beta distribution into gamma distribution

How can I convert a Beta Distribution to a Gamma Distribution? Strictly speaking, I want to transform parameters of a Beta Distribution to parameters of the corresponding Gamma Distribution. I have mean value, alpha and beta parameters of a Beta Distribution and I want to transform them to those of a Gamma Distribution.

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What do you mean by "converting" ? The Beta disrtribution is supported on $(0,1)$ whereas the Gamma distribution is supported on $(0,+\infty)$ – Siméon Jan 16 '13 at 11:42
@Ju'x the intervals $(0,1)$ and $(0,+\infty)$ are homeomorphic. – MathOverview Jan 16 '13 at 11:55
@Elias Sure, but what does the question mean by "corresponding"? There are infinitely many homeomorphisms between $(0,1)$ and $(0,+\infty)$, which lead to infinitely many possible probability distributions on $(0,+\infty)$ for each beta distribution--including every possible gamma distribution. – Jonathan Christensen Jan 16 '13 at 16:29
If I am right there is a relation between these distribution. I wanted to know how to convert parameters of beta distribution to those of gamma's. – Kaveh Jan 17 '13 at 8:07

Let $X_a$ and $X_b$ denote independent gamma random variables with respective parameters $(a,c)$ and $(b,c)$, for some nonzero $c$. Then $\dfrac{X_a}{X_a+X_b}$ is a beta random variable with parameter $(a,b)$.