On Thu, 26 Mar 2009, Jason Rupert wrote:
The R code below produces (after running for a few minutes on a decent
computer) the plot shown at the following location:
http://n2.nabble.com/Is-there-a-physical-and-quantitative-explanation-for-this-plot--td2542321.html
I'm just taking the mean of a given set of random variables, where the
set size is increased. There appears to be a quick convergence and then
a pretty steady variance out to a set size of 10,0000.
I don't have time to study your code, but it sounds like you are taking
random normal variables with mean 0 and variance 1, but then taking the
mean for sets of those. We know exactly the distribution for the mean of
the "set" (a.k.a., "sample"). The mean has a normal distribution with
mean 0 and variance 1/N where N is the size of the sample. When you allow
N to vary, you produce a mixture of random normal variables all having
mean 0 but with different variances. The plot you show looks correct --
the distributions in the mixture that have small variance pile up in the
middle, while those with greater variance form the long tails. You could
get a lot of different shapes depending ont he distribution of N. But
save yourself some time. Instead of making N normal variables and taking
the mean, just make one and divide it by sqrt(N) -- that will give you
*exactly* the same result.
Your graph looks a little weird - first, why turn it sideways? We
normally plot density on the ordinate, not on the abscissa. Second, there
is a thick black bar on the left, but that seems to be an artifact because
at least half of it is below zero -- how can that happen?
Mike
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