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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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    $\begingroup$ What do you mean by "converting" ? The Beta disrtribution is supported on $(0,1)$ whereas the Gamma distribution is supported on $(0,+\infty)$ $\endgroup$ – Siméon Jan 16 '13 at 11:42
  • $\begingroup$ @Ju'x the intervals $(0,1)$ and $(0,+\infty)$ are homeomorphic. $\endgroup$ – MathOverview Jan 16 '13 at 11:55
  • $\begingroup$ @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. $\endgroup$ – Jonathan Christensen Jan 16 '13 at 16:29
  • $\begingroup$ 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. $\endgroup$ – Kaveh Jan 17 '13 at 8:07
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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 $(a,b)$.

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You can make a transformation as U = X + Y and V = X/(X+Y) where X and Y both are having gamma distribution with parameters aplha, Beta respectively. Out of these two, U will be Gamma distribution with parameters aplha + beta and V will be a Beta Distribution of first kind with parameter alpha, beta.

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if x denotes beta distribution of 1st kind with parameters @ and 1 then -logx will follow gamma distribution with parameters @ and 1

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