 My Math Forum Posterior Distribution from Beta Density with Exponential Prior
 User Name Remember Me? Password

 Advanced Statistics Advanced Probability and Statistics Math Forum

 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
Senior Member

Joined: Sep 2015
From: USA

Posts: 2,574
Thanks: 1422

Quote:
 Originally Posted by Denis posterior = ass ?
corner Tags beta, density, distribution, exponential, posterior, prior Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post calypso Advanced Statistics 0 December 29th, 2015 01:14 AM lotharson Advanced Statistics 1 August 30th, 2015 03:34 PM MathHatesMe Advanced Statistics 14 December 7th, 2014 03:59 AM wannabe1 Advanced Statistics 4 February 27th, 2013 05:36 PM Scoriger Advanced Statistics 0 January 31st, 2010 04:24 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top       