Actuarial Outpost Questions for Dr. Weishaus
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#1
05-15-2009, 11:28 AM
 AUM Member Join Date: May 2006 Posts: 99
Questions for Dr. Weishaus

How do you solve a normal/lognormal or lognormal/lognormal (model/prior) problem? I didn't see this combination addressed in your manual and according to what you wrote for the normal/normal pair, none of the textbooks actually address this type of questions.
How do you solve a kernel smoothing question which is neither triangular, uniform nor gamma? The only thing given was the density function.

This exam was absolutely insane...

Thanks!
#2
05-15-2009, 11:29 AM
 carryme ...:illllllli:.. Join Date: Feb 2005 Posts: 1,939

You're getting too specific dude. Moderator1 is around, watching you very closely.
__________________
...:illlllllli:...
#3
05-15-2009, 11:38 AM
 Abraham Weishaus Member SOA AAA Join Date: Oct 2001 Posts: 6,194

I answered the second question, but that answer was deleted. Perhaps this answer won't be deleted: the ASM manual covers some other possibiities for kernels, as have some old released exam questions. See exercises 24.6 and 24.15. An exam question asking a question on an arbitrary kernel should not puzzle you, and is testing to see if you can go beyond formulas.
#4
05-15-2009, 11:41 AM
 pcramirez Member Join Date: May 2006 Posts: 48

Quote:
 Originally Posted by AUM How do you solve a normal/lognormal or lognormal/lognormal (model/prior) problem? I didn't see this combination addressed in your manual and according to what you wrote for the normal/normal pair, none of the textbooks actually address this type of questions. How do you solve a kernel smoothing question which is neither triangular, uniform nor gamma? The only thing given was the density function. This exam was absolutely insane... Thanks!
Integrate the kernel density function, and multiply that integral by the probability of that point being chosen (1/N, N the number of points). Also, you could determine the bandwidth by looking at the density function. I had a better written response, but I just shortened it in hopes that it won't be deleted. If you want more specifics, you can PM me .
#5
05-15-2009, 11:51 AM
 AUM Member Join Date: May 2006 Posts: 99

Quote:
 Originally Posted by Abraham Weishaus I answered the second question, but that answer was deleted. Perhaps this answer won't be deleted: the ASM manual covers some other possibiities for kernels, as have some old released exam questions. See exercises 24.6 and 24.15. An exam question asking a question on an arbitrary kernel should not puzzle you, and is testing to see if you can go beyond formulas.
#6
05-15-2009, 11:58 AM
 AUM Member Join Date: May 2006 Posts: 99

Quote:
 Originally Posted by pcramirez Integrate the kernel density function, and multiply that integral by the probability of that point being chosen (1/N, N the number of points). Also, you could determine the bandwidth by looking at the density function. I had a better written response, but I just shortened it in hopes that it won't be deleted. If you want more specifics, you can PM me .
Thanks!!
#7
05-15-2009, 02:11 PM
 Abraham Weishaus Member SOA AAA Join Date: Oct 2001 Posts: 6,194

Quote:
 Originally Posted by AUM Thanks!!
About your other question - of course I have no idea what the exam question was. But if X is lognormal, then ln X is normal. If the parameters of the lognormal are theta and v and the mean theta varies according to another normal distribution with parameters mu and a, then the posterior for ln X is normal (by the normal/normal conjugate prior), and then X itself is lognormal with the same parameters as the posterior ln X.

In general with conjugate priors, you can do reparametrizations like that. In Loss Models 3rd edition, instead of exponential/inverse gamma conjugate prior, they feature exponential/gamma. They simply use 1/theta as the exponetial's parameter instead of theta. If X is gamma, then X^{-1} is inverse gamma, so it's the same idea.
#8
05-15-2009, 03:56 PM
 AUM Member Join Date: May 2006 Posts: 99

Quote:
 Originally Posted by Abraham Weishaus About your other question - of course I have no idea what the exam question was. But if X is lognormal, then ln X is normal. If the parameters of the lognormal are theta and v and the mean theta varies according to another normal distribution with parameters mu and a, then the posterior for ln X is normal (by the normal/normal conjugate prior), and then X itself is lognormal with the same parameters as the posterior ln X. In general with conjugate priors, you can do reparametrizations like that. In Loss Models 3rd edition, instead of exponential/inverse gamma conjugate prior, they feature exponential/gamma. They simply use 1/theta as the exponetial's parameter instead of theta. If X is gamma, then X^{-1} is inverse gamma, so it's the same idea.
#9
05-15-2009, 04:01 PM
 atkinsmt Member CAS Join Date: Nov 2008 Location: Houston, TX Studying for CAS 8 College: University of Waterloo Posts: 804

Quote:
 Originally Posted by AUM thanks again for your clarification!
Are you going to remember all that for next time? Oh wait, you won't need to because something more evil awaits.
#10
05-15-2009, 04:04 PM
 badmaj5 Member CAS Join Date: Sep 2005 Location: Chicago, IL Posts: 454

I'll worry about remembering it in a few months. I feel like this will not be the end of that topic.

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