fat tailed distributions
Normal vs. Fat-tailed Distributions
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Normal vs. Fat-tailed Distributions
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Re: Normal vs. Fat-tailed Distributions
#2It would be awesome if these could be embedded in Wikipedia somehow.
Re: Normal vs. Fat-tailed Distributions
#3It would be awesome if these could be embedded in Wikipedia somehow.
My laptop's fan says that may not be advisable.
P.S. sometimes people overlook how a well-drawn illustration may be superior to photos or video; think anatomical drawings, for instance. In this case I feel the lack of two simple curves superimposed to illustrate the point about the variance.
Re: Normal vs. Fat-tailed Distributions
#4the [edit: outer envelope of the] walk should slowly deviate from zero, shouldn't it (the variance of the sum increases with time / a random walk is a walk)? what i am seeing is returning to zero much more strongly than i would have expected. what is the prng that you are using? i suspect it's not that great.
Re: Normal vs. Fat-tailed Distributions
#5This is great, but I have a slight complaint.
Sliding the kurtosis indicator changes the left distribution, which makes sense. However, it also changes the appearance of the right, normal distribution, which is misleading. Normal distributions have [EDIT: constant] kurtosis. I realize that the appearance is changing because the scale is changing so that the max is always pegged. However, it might be less confusing if the scale remained static and the height of the left distribution simply changed, since that would be a more accurate representation of what's actually happening. That would obscure some details, but I don't think the precise details of the heights of each bar in the distribution are really the point of this page.
Re: Normal vs. Fat-tailed Distributions
#6This is great, but I have a slight complaint. Sliding the kurtosis indicator changes the left distribution, which makes sense. However, it also changes the appearance of the right, normal distribution, which is misleading. Normal distributions have [EDIT: constant] kurtosis. I realize that the appearance is changing because the scale is changing so that the max is always pegged. However, it might be less confusing if…
yeah i gave myself some grief about that aspect but ultimately decided different scales was more misleading. could go either way.
also, the kurtosis of a normal distribution is 3, not 0.
Re: Normal vs. Fat-tailed Distributions
#7This is great, but I have a slight complaint. Sliding the kurtosis indicator changes the left distribution, which makes sense. However, it also changes the appearance of the right, normal distribution, which is misleading. Normal distributions have [EDIT: constant] kurtosis. I realize that the appearance is changing because the scale is changing so that the max is always pegged. However, it might be less confusing if…
yeah i gave myself some grief about that aspect but ultimately decided different scales was more misleading. could go either way. also, the kurtosis of a normal distribution is 3, not 0.
Many statistical packages (SAS IIRC) subtract 3 from the kurtosis to set a normal distribution at 0. This is an infuriating tendency.
Re: Normal vs. Fat-tailed Distributions
#8This is great, but I have a slight complaint. Sliding the kurtosis indicator changes the left distribution, which makes sense. However, it also changes the appearance of the right, normal distribution, which is misleading. Normal distributions have [EDIT: constant] kurtosis. I realize that the appearance is changing because the scale is changing so that the max is always pegged. However, it might be less confusing if…
yeah i gave myself some grief about that aspect but ultimately decided different scales was more misleading. could go either way. also, the kurtosis of a normal distribution is 3, not 0.
Yes, on your scale it appears that is the case. Most definitions I've seen have a -3 constant to zero out the normal, but if you say that's weird I won't argue. Incidentally, why didn't you extend the kurtosis scale to allow for a platykurtic distribution?
EDIT: to the original question, I'm not suggesting the distributions should have different scales, but rather that the scale of both should be static.
Re: Normal vs. Fat-tailed Distributions
#9From the article: "Both distributions below have standard deviations of 1"
I thought fat tailed distributions don't have a variance. But apparently I'm using the term in a stricter sense than other people. See http://en.wikipedia.org/wiki/Fat-tailed_distribution#Definit... for details if you were wondering, too.
Re: Normal vs. Fat-tailed Distributions
#10From the article: "Both distributions below have standard deviations of 1" I thought fat tailed distributions don't have a variance. But apparently I'm using the term in a stricter sense than other people. See http://en.wikipedia.org/wiki/Fat-tailed_distribution#Definit... for details if you were wondering, too.
Most statisticians have their own definition of fat-tailed, I like the definition you linked to (polynomial decay), but it is not universally accepted/known. These fat-tailed distributions will have a variance as long as they decay faster than x^(-3).