# Estimation

Printable View

• February 3rd 2011, 06:46 PM
holly123
Estimation
suppose that the prior distribution of some parameter theta is a gamma distribution for which the mean is 10 and the variance is 5. determine the prior pdf of theta
• February 3rd 2011, 06:55 PM
theodds
Unless there is something I'm missing, there doesn't seem to be a question here. They tell you the distribution of theta. You know the mean and variance of a gamma; solve for the usual parameters.
• February 3rd 2011, 06:57 PM
pickslides
Consider parameters $\displaystyle k, \theta$ such that $\displaystyle \mu = k\theta$ and $\displaystyle \sigma^2 =k\theta^2$

You are told $\displaystyle k\theta =10 , k\theta^2 = 5$ solve for $\displaystyle k, \theta$

The pdf will then be $\displaystyle P(x) =\frac{x^{k-1}e^{\frac{-x}{\theta}}}{\Gamma (k)\theta^k}$
• February 3rd 2011, 06:57 PM
holly123
is that really all there is to it?
• February 3rd 2011, 07:07 PM
pickslides
That's what I read.

The whole 'prior' thing made it sounds bigger than what it was. But everything described was prior so it all links together easily.