Re: Mean and Variance
- From: "John D'Errico" <woodchips@xxxxxxxxxxxxxxxx>
- Date: Sun, 27 Jan 2008 14:00:03 +0000 (UTC)
"Hesham " <heltaher.nospam@xxxxxxxxxxxxx> wrote in message
<fni1n9$c4b$1@xxxxxxxxxxxxxxxxxx>...
Hi,
I have a polynomial of x(1), x(2),...x(n).
each variable x has a normal distribution around a mean value.
How can I calculate the MEAN and VARIANCE of the polynomial?
Thank you
This is a problem called "statistical tolerancing"
by some. Others call it "propagation of errors".
There are several different methods one can
use. The simplest is to assume a linear (first
order Taylor series) approximation for your
polynomial. Then if your variables are normally
distributed, then the mean and variance of a
linear combination of normal variables is simple
to compute.
You can also use second order Taylor series
approximations, though this is a bit nastier
to compute.
Other ways to do this are to use Taguchi
methods, or modified Taguchi methods,
which can be shown to be simply numerical
integrations of a Gauss-Hermite class. (I got
a couple of papers on this topic many years
ago.) This Taguchi class of methods is often
surprisingly easy to use.
Finally, you can use simulation methods to
compute the approximate distribution of the
result. This is just Monte Carlo Simulation.
HTH,
John
.
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