
Advanced Statistics Advanced Probability and Statistics Math Forum 
 LinkBack  Thread Tools  Display Modes 
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: $f(x\theta)=\theta x^{\theta1}$ 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 $$f(\thetax)\propto f(x\theta)\pi(\theta)=\frac{\theta x^{\theta1}e^{\theta/2}}{2}$$ 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: 490 Thanks: 164 
Looks like a gamma.

February 14th, 2018, 08:41 AM  #3 
Senior Member Joined: Sep 2015 From: USA Posts: 2,094 Thanks: 1088 
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: 13,122 Thanks: 913 
posterior = ass ?

February 14th, 2018, 01:04 PM  #5 
Senior Member Joined: Sep 2015 From: USA Posts: 2,094 Thanks: 1088  

Tags 
beta, density, distribution, exponential, posterior, prior 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Prior distribution  calypso  Advanced Statistics  0  December 29th, 2015 01:14 AM 
Prior probability distribution for k [a;b]  lotharson  Advanced Statistics  1  August 30th, 2015 03:34 PM 
Proof beta distribution = exponential when B =0  MathHatesMe  Advanced Statistics  14  December 7th, 2014 03:59 AM 
Prior And Posterior  wannabe1  Advanced Statistics  4  February 27th, 2013 05:36 PM 
[HELP] Gamma distribution & Beta distribution  Scoriger  Advanced Statistics  0  January 31st, 2010 04:24 PM 