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February 13th, 2018, 03:49 PM   #1
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Exclamation Posterior Distribution from Beta Density with Exponential Prior

Let $X_1,...,X_n$ be iid random variables with a common density function given by:

$f(x|\theta)=\theta x^{\theta-1}$

for $x\in[0,1]$ and $\theta>0$.

Put a prior distribution on $\theta$ which is $EXP(2)$, where $2$ is the mean of the exponential distribution. Obtain the posterior density function of $\theta$. Do you recognize this distribution?

Clearly $f(x|\theta)$ is a beta distribution. So this implies that the posterior distribution is

$$f(\theta|x)\propto f(x|\theta)\pi(\theta)=\frac{\theta x^{\theta-1}e^{-\theta/2}}{2}$$

But I don't really recognize the distribution at all. Was my calculation incorrect? If not, what is the name of this distribution?
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February 13th, 2018, 09:35 PM   #2
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Looks like a gamma.
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February 14th, 2018, 09:41 AM   #3
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Was it you that got this answered over at Stack Exchange? Are you all set now?
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February 14th, 2018, 01:28 PM   #4
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posterior = ass ?
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February 14th, 2018, 02:04 PM   #5
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Quote:
Originally Posted by Denis View Post
posterior = ass ?
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