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#1
10-20-2011, 10:07 AM
 psu602 Member SOA Join Date: May 2009 Location: Florence, KY Studying for FAP College: Penn State Univerisity 2010 Favorite beer: Cheerwine Posts: 354
Variance of Kernels

Occassionally, a question will ask the variance of a uniform kernel distribution. I'm becoming very comfortable with this type of problem. The formula I use is:

Variance(Sample) + (2b)^12

I think this is derived from the Law of Total Variation.

Anyway, is it possible that they would ask about the Variance of a Triangular kernel? What would be the formula?
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#2
10-20-2011, 10:20 AM
 daaaave David Revelle Join Date: Feb 2006 Posts: 2,487

For the uniform kernel, you mean (2b)^2/12 = b^2/3, not (2b)^12.

For a triangular kernel, instead of (2b)^2/12 you could calculate the variance of a random variable whose density is the triangle associated with the kernel (i.e., symmetric about the mean, peak height is 1/b). My recollection is that you have access to my seminar, so you could also see B.2 #25 for more details. It turns out that we get 1/2 of the variance from the uniform distribution, i.e., b^2/6.
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#3
10-20-2011, 10:21 AM
 psu602 Member SOA Join Date: May 2009 Location: Florence, KY Studying for FAP College: Penn State Univerisity 2010 Favorite beer: Cheerwine Posts: 354

Correct, (2b)^2 / 12

Thanks Dave!
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#4
10-20-2011, 10:39 AM
 dickmwong Member SOA Join Date: Mar 2011 College: University of Hong Kong; London School of Economics Posts: 212

the formula for a triangular one is variance of original data + b^2 /6
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#5
10-20-2011, 10:57 AM
 am_vanquish Member SOA Join Date: Mar 2007 Studying for the zombie apocalpyse Favorite beer: Smithwick's Posts: 656

Is this really something we need to know? I don't recall ever seeing one of these problems ....

Just searched the SOA 289 pdf & didn't find a single problem with variance of kernel.

Search the TIA 240 and found only one problem (# 214), which asks for the coefficient of variation for a uniform kernel.

I'm not trying to minimize your question - I'm sure you have a reason to ask. Just wondering if that reason is because it comes up frequently on exams or if you're just trying to be super over-prepared.
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#6
10-20-2011, 11:10 AM
 Jonnyb373 Member Join Date: Oct 2008 Posts: 46

Quote:
 Originally Posted by am_vanquish Is this really something we need to know? I don't recall ever seeing one of these problems .... Just searched the SOA 289 pdf & didn't find a single problem with variance of kernel. Search the TIA 240 and found only one problem (# 214), which asks for the coefficient of variation for a uniform kernel. I'm not trying to minimize your question - I'm sure you have a reason to ask. Just wondering if that reason is because it comes up frequently on exams or if you're just trying to be super over-prepared.
It does come up frequently and should be easy points.
#7
10-20-2011, 11:35 AM
 wheez17 Member Join Date: Oct 2010 Posts: 58

cool did not know how to do variance of triangular before:

Triangular =
variance(sample) + ((2b)^2/12))*.5

Uniform
variance(sample) + ((2b)^2/12))
#8
10-20-2011, 11:39 AM
 psu602 Member SOA Join Date: May 2009 Location: Florence, KY Studying for FAP College: Penn State Univerisity 2010 Favorite beer: Cheerwine Posts: 354

Quote:
 Originally Posted by am_vanquish Is this really something we need to know? I don't recall ever seeing one of these problems .... Just searched the SOA 289 pdf & didn't find a single problem with variance of kernel. Search the TIA 240 and found only one problem (# 214), which asks for the coefficient of variation for a uniform kernel. I'm not trying to minimize your question - I'm sure you have a reason to ask. Just wondering if that reason is because it comes up frequently on exams or if you're just trying to be super over-prepared.
I don't think it comes up very frequently. However, it takes up .000000000001% of my brain to remember that it's the same as a uniform except for 1 factor. I'm not super over-prepared, but I don't want to miss easy points.

I'm okay with not knowing Anderson-Darling, because that's not worth it imo.
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#9
10-20-2011, 11:42 AM
 am_vanquish Member SOA Join Date: Mar 2007 Studying for the zombie apocalpyse Favorite beer: Smithwick's Posts: 656

Gotcha. I might be wound up a bit too tightly as the exam approaches. Seems like I'm constantly telling myself "I have to know that TOO?" over the past few days.
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