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-   -   Posterior Distribution from Beta Density with Exponential Prior (http://mymathforum.com/advanced-statistics/343410-posterior-distribution-beta-density-exponential-prior.html)

John Travolski February 13th, 2018 02:49 PM

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?

Micrm@ss February 13th, 2018 08:35 PM

Looks like a gamma.

romsek February 14th, 2018 08:41 AM

Was it you that got this answered over at Stack Exchange? Are you all set now?

Denis February 14th, 2018 12:28 PM

posterior = ass ?

romsek February 14th, 2018 01:04 PM

Quote:

Originally Posted by Denis (Post 588544)
posterior = ass ?

corner


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