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Sweeting text page 379 on Poisson MLE

A

ALEX_AK

Member
Hello,
I cant seem to derive the f(dx)=0.0888 where dx =20.

qx=-9.05+0.08x
q(80)=-9.05+0.08(80)=-2.53
How can qx be greater than 1? Is the text missing out something?

Can anyone derive f(dx) where dx=20?
 
Hi Alex

This is a good question, had to stare at it for a while before the penny finally dropped! The model for qx is a log-linear function of age.

Therefore:

ln qx = a + bx
qx = exp(a+bx)

With x = 80, a = -9.05 and b = 0.0815, I get qx = 0.079659.

Then yx = qx * lx = 0.079659 * 250 = 19.91476.

And f(dx) = [exp(-19.91476) * 19.91476^20]/20! = 0.0888

This is a type of generalised linear model from CT6.

Hope this helps :)
Anna
 
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