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Old 12-12-2018, 02:51 PM
uyttrefds uyttrefds is offline
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Last edited by uyttrefds; 12-13-2018 at 10:49 AM..
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Old 12-12-2018, 05:15 PM
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Originally Posted by uyttrefds View Post
Given a model is inverse Gamma and prior is Gamma, calculate the Bayesian premium and credibility premium (given sample size is n).

The concrete example given is:
X1,X2,Xn∼IG(α=4,θ)θ∼Γ(α=50,θ=5000)n=25

From this,
Z=100103, Pc=1008+50103, and a Bayesian premium of:
(4n+0.5)[(α−1)(.01+∑xi)]

However, not much work is shown, and I'm struggling to figure out a general formula for this case.

How can I apply this to a general formula for Bayesian and Credibility premium with Inverse Gamma and a Gamma prior? Thanks so much!
What you have written makes no sense. Z must be between 0 and 1, and you wrote that Z = 100103. Can't be.

Also, you can't get the credibility premium (Buhlmann?) without knowing the observations.

Finally, you write the Bayesian estimate as a formula in "a" and "n", but previously wrote that a=4 once and a=50 another time and n=25.

Might you look again at the problem and then carefully restate your question?
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Old 12-12-2018, 08:14 PM
uyttrefds uyttrefds is offline
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Old 12-12-2018, 09:14 PM
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The data and answer still make little sense. Might you scan the printed version of the problem and "solution" and post it? I suspect you have typed some things incorrectly.
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