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Short-Term Actuarial Math Old Exam C Forum

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  #1  
Old 06-19-2018, 02:33 PM
cashcrazy cashcrazy is offline
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Hi, I tried doing this question a different way. Namely, using the Buhlmann credibility estimate formula: Pc=Zxbar+(1-Z)uhat. In this situation, is using the Buhlmann credibility estimate viable?

I got:
xbar=3/6
v=EPV=E[Var(X|type of risk)]=0.119
a=VHM=Var(E[X|type of risk])=0.0085.
uhat=E[E[X|type of riks]]=0.15.

Thank you for your help.
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Old 06-19-2018, 02:39 PM
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The question asks for the posterior probability. If it had asked for the Buhlman credibility estimate you would have used that. The two estimates are not the same except for special cases.
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Old 06-19-2018, 02:48 PM
cashcrazy cashcrazy is offline
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Hi, thanks for your reply.

Would you be able to tell me about the special cases? Thank you.
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Old 06-19-2018, 02:48 PM
jas1290 jas1290 is offline
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The Buhlmann credibility estimate would not be equal to the posterior probability here. A more detailed explanation is that the EPV and VHM are calculated prior to knowing the particular observation(s), so since we want the poster probability; this leads to the wrong answer if calculated using Buhlmann credibility estimate.

Buhlmann = Bayesian for Poisson/Gamma, Binomial/Beta, Normal/Normal. Basically in a conjugate prior situation.
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Old 06-19-2018, 04:26 PM
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In general the likelihood has to be linear exponential. The other possibility would be exponential/gamma or exponential/inverse gamma depending upon whether the exponential parameter was in the numerator or denominator.
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Old 06-19-2018, 05:19 PM
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Jim Daniel Jim Daniel is offline
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Quote:
Originally Posted by jas1290 View Post
The Buhlmann credibility estimate would not be equal to the posterior probability here. A more detailed explanation is that the EPV and VHM are calculated prior to knowing the particular observation(s), so since we want the poster probability; this leads to the wrong answer if calculated using Buhlmann credibility estimate.

Buhlmann = Bayesian for Poisson/Gamma, Binomial/Beta, Normal/Normal. Basically in a conjugate prior situation.
Careful. Not in ALL conjugate priors.
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