If S2 is the sample variance based on a sample of size n from a normal population, we know that (n l)S2 Iuml 2 has a X2n 1 distribution The conjugate prior for Iuml 2 is the inverted gamma pdf, IG( Icirc plusmn , Icirc sup2 ), given by where Icirc plusmn and Icirc sup2 are positive constants Show t...

Let t s 2 and 2 Because n 1S 2 2 X 2 n1 we have With as given we h ...

If S2 is the sample variance based on a sample of size n from a normal population,

Question:

If S2 is the sample variance based on a sample of size n from a normal population, we know that (n - l)S2/Ïƒ2 has a X2n-1 The conjugate prior for Ïƒ2 is the inverted gamma pdf, IG(Î±, Î²), given by

where Î± and Î² are positive constants. Show that the posterior distribution of Ïƒ2 is

Find the mean of this distribution, the Bayes estimator of Ïƒ2.

Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...