April 2006 Q8

[srivadana]

Hi,

This is reg Q8:

I am not sure why in the solution he mentioned X1= (n1 * Y1 )/c

I was thinking about this question this way:

For year 1:
The no of policies = n1
Claim amount is fixed = c per policy
So total no of claims = n1 * c

Average claim amount = Y1

I got stuck aftee this, I dint know how to go about f(y1,y2|theta) from here.

Can someone help?

 

[John Lee]

Hi,

This is reg Q8:

I am not sure why in the solution he mentioned X1= (n1 * Y1 )/c

I was thinking about this question this way:

For year 1:
The no of policies = n1
Claim amount is fixed = c per policy
So total no of claims = n1 * c

Average claim amount = Y1

I got stuck aftee this, I dint know how to go about f(y1,y2|theta) from here.

Can someone help?

See my answer to your other post for the correct average number of claims. Your n1c simply gives the amount of the claims if each policy makes one claim.

we get f(y1,y2|theta) using the posterior is proportional to the likelihood times the prior.

 

[jm_kinuthia]

Please explain to me how the second equation comes about in the solution to part (iii).

 

[John Lee]

Please explain to me how the second equation comes about in the solution to part (iii).

I assume you're referring to the examiners report rather than our ASET or revision notes answer.

\( \frac{Y_3 n_3}{c(1+r^2)} \) has a \(Poi(n_3 \theta ) \) distribution.

From this you can get \( E(Y_3) = \theta c (1 + r)^2 \)

In the examiners second equation they have this with the \( \theta \) replaced by its posterior estimate - which is the third term in the product.

 

[jm_kinuthia]

They have based the estimate on the quadratic loss function thus taking the mean of the posterior. Is there a reason why they did not use the other loss functions to get an estimate ?