Variance of Kernels

[psu602]

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?

[daaaave]

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.

[psu602]

Correct, (2b)^2 / 12

Thanks Dave!

[dickmwong]

the formula for a triangular one is variance of original data + b^2 /6

[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.

[Jonnyb373]

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.

[wheez17]

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

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

Uniform
variance(sample) + ((2b)^2/12))

[psu602]

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.

[am_vanquish]

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.