Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: Gaussian dist. Integral



At 20:47 5/11/99 -0700, Mike Wilson wrote:
... the integral which results in the normal or
gaussian distribution equation (about .4 e^(-.5 z^2) , where z is defined
in terms of the population mean and standard deviation).

...point me to a source which explains the
integral and initial equation needed to derive the equation. It would be
very nice if the source was a url since my local library resources are
limited.

Mike Wilson

Mike's note reminds me to take care what I wish for....
A pointer from YorkU, Toronto leads to this:

http://www.stat.ufl.edu/vlib/statistics.html

This is an extensive compendium!
Choosing the normal distribution:

http://ubmail.ubalt.edu/~harsham/stat-data/opre330.htm#rNormal

If one is persistant in passing through great waterfalls of material,
one can arrive at this little morsel:
---------------------------------------------------------------------
Comments: Many methods of statistical analysis presume normal
distribution. A so-called Generalized Gaussian distribution
has the following pdf:

A.exp[-B|x|^n], where A, B, n are constants. For n=1 and 2
it is a Laplacian and Gaussian distribution respectively.
This distribution approximates reasonably good data in some image
coding application.


----------------------------------------------------------------------

I could not summon the perseverence to sieve the many contributions
at varying levels for a more extensive version like John Mandel's
"Statistical Analysis of Experimental Data" Dover ISBN 0-486-64666-1
Para 3.9, pp48 on "Normal Distribution"
where one proceeds from
f(x) = 1/(SD.sqrt(2.pi)) exp(-1/2 ((x - mean)/SD)^2) (eq 3.28)

to

probability = 1/sqrt(2.pi) exp(-y^2/2) dy (eq 3.32)

by stages....


brian whatcott <inet@intellisys.net>
Altus OK