You mean a one-dimensional Gaussian? In that case, the normalisation
constant will be given (more or less) by the cumulative distribution
function of the Gaussian, which has no expression, to my knowledge, in terms
of elementary functions. However, it is tabulated all over the place, and
Matlab for example, has it as a built in function.
In more detail: if you have a Gaussian with mean m and variance s^{2}, and
the space under consideration is from x = a to x = b, then the normalisation
constant is:
Z(a, b) = \int_{a}^{b} exp - (x - m)^{2}/2s^{2} dx
By changing variables from x to z = (x - m)/s, this becomes:
Z(a, b) = s. \int_{a - m)/s}^{b - m)/s} exp - z^{2}/2 dz
If we define the following function:
E(y) = \int_{-infty}^{y} exp - z^{2}/2
then the normalisation is given by
Z(a, b) = s.[E((b - m)/s) - E((a - m)/s)]
It is the values of E, or functions very closely related to it, for example
erf, that you should be able to find in Matlab. E is closely related to the
incomplete Gamma function.
The Laplace distribution is similar but easier, because the cumulative
distribution function is expressible in terms of elementary functions:
http://mathworld.wolfram.com/LaplaceDistribution.html.
Ian Jermyn.
"Chia C Chong" <[EMAIL PROTECTED]> wrote in message
news:aqb42h$bvf$1@;scotsman.ed.ac.uk...
> Hi!
>
> Could anyone give me some references and books on how the normalization
> constant for the truncated Gaussian PDF and truncated Laplacian PDF can be
> done.
>
> Thanks very much.
>
> CCC
>
>
.
.
=================================================================
Instructions for joining and leaving this list, remarks about the
problem of INAPPROPRIATE MESSAGES, and archives are available at:
. http://jse.stat.ncsu.edu/ .
=================================================================
