My Math Forum Posterior Distribution from Beta Density with Exponential Prior

 February 13th, 2018, 02:49 PM #1 Senior Member   Joined: Oct 2015 From: Antarctica Posts: 128 Thanks: 0 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?
 February 13th, 2018, 08:35 PM #2 Senior Member   Joined: Oct 2009 Posts: 882 Thanks: 339 Looks like a gamma.
 February 14th, 2018, 08:41 AM #3 Senior Member     Joined: Sep 2015 From: USA Posts: 2,574 Thanks: 1422 Was it you that got this answered over at Stack Exchange? Are you all set now?
 February 14th, 2018, 12:28 PM #4 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 posterior = ass ? Thanks from Joppy
February 14th, 2018, 01:04 PM   #5
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Quote:
 Originally Posted by Denis posterior = ass ?
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 Tags beta, density, distribution, exponential, posterior, prior

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