Re: Multisets of integers with equal sums, sums-of-squares, etc.
- From: "David C. Ullrich" <dullrich@xxxxxxxxxxx>
- Date: Sun, 6 Apr 2008 19:30:04 +0000 (UTC)
On Sun, 6 Apr 2008 15:30:12 +0000 (UTC), "joeshipman@xxxxxxx"
<JoeShipman@xxxxxxx> wrote:
The multisets {3,3} and {1,1,4} have equal sums and equal sums-of-
squares. What's the smallest example of two multisets of integers
which have the same sums-of-nth-powers for n=1,2,3? What's the
smallest example for n=1,2,3,4?
I am interested in this because multisets with equal sums and sums-of-
squares have the same mean and standard deviation.
So the mean of the elements of {1,1,4} is 3 and the standard
deviation is 0?
Sampling with
replacement from these multisets ought to converge to the same thing
by the Central Limit Theorem, but I want to illustrate how the rate of
convergence depends on higher moments, using examples that are
numerically simple.
It shouldn't be hard to construct simple example of distributions
that _do_ have idential means and standard deviations...
David C. Ullrich
.
- References:
- Multisets of integers with equal sums, sums-of-squares, etc.
- From: joeshipman@xxxxxxx
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