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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.

Vobo
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Kaveh
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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. – Elias Costa 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 08:07
  • https://math.stackexchange.com/a/190695/321264 – StubbornAtom Apr 02 '20 at 06:32

3 Answers3

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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 $(a,b)$.

Did
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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.

LALIT SALUNKHE
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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

rukhsar khan
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