Buhlmann credibility

[Jake_The_Snake_724]

I am working on lesson 48 in the ASM manual 13th ed. and I am having trouble finding the credibility expectation.

The formula is
Pc= mu +Z(xbar-mu)

I know how to calculate mu and Z, but for some reason I can't figure out how to get xbar.

Here is an example

48.10
An urn is selected at random and four balls are selected from the urn with replacement. The total of the values is 2. Four more balls are selected from the same urn.

They also gave a table but I am pretty sure I don't need that to calculate xbar. If anyone wants to see it I can type it up. This is probably a dumb question, but it has been the only thing screwing me up in this section. I looked in previous sections but it isn't clicking. Just when I think I get it, it doesn't work for the next problem.


Thanks in advance

[truonda]

In Layman terms try to think of xbar for what it is: an average. Try to look for an average of something based on the information they give you. In your example the total number of balls drawn is four and the total value of those balls is two which means that on average a ball drawn has a value of 0.5.

When you calculate Pc you have to remember that it is an estimate for a single ball so since four more balls are drawn then you will need to multiply Pc by four to get the answer.

[Jake_The_Snake_724]

Thanks!
That's what I have been thinking of it as, an average. Since like you said, that is what it is! I wound up getting 0.5 also, but the solution says it is 2. For some reason I keep getting it backwards. But I do see what you are saying.

Pc=2.1+(83/162)[2-2.1]
is what they have as the answer.

[truonda]

Could you type out the question?

[Jake_The_Snake_724]

Four Urns contain balls marked with either 0 or 1 in the proportions described below
Urn Marked 0 Marked 1
A 70% 30%
B 70 30
C 30 70
D 20 80

An urn is selected at random and four balls are selected from the urn with replacement. The total of the values is 2. Four more balls are selected from the same urn. Calculate the expected total of the four balls using Buhlmann's credibility formula.

[truonda]

Maybe it's a notational thing but for me Pc should be equal to 0.525 + 83/162 x (0.5 - 0.525) and the question is asking you to find 4 x Pc. Hope that helps.

[Force of Interest]

Originally Posted by Jake_The_Snake_724

Thanks!
That's what I have been thinking of it as, an average. Since like you said, that is what it is! I wound up getting 0.5 also, but the solution says it is 2. For some reason I keep getting it backwards. But I do see what you are saying.

Pc=2.1+(83/162)[2-2.1]
is what they have as the answer.

The solution is using 4 balls as an exposure unit. If you use .5 as your xbar then you are using 1 ball as an exposure unit. Either one will get you the right answer as long as you're consistent (i.e. mu and z for the exposure unit).