# Thread: Approximation of gaussian normalization factor

1. ## Approximation of gaussian normalization factor

hey,
im working with a gaussian distribution
$\displaystyle P_\mu (x) = \frac{1}{A} e^{ - \frac{(x-\mu)^2}{2\sigma^2} }$
on a finite domain [a,b]. This of course means that the normalization factor A depends on $\displaystyle \mu$ (as well as $\displaystyle \sigma$). I care less about accuracy and more about getting an analytic answer that does not involve integrals, and so looking for a way to approximate A. Namley, I'm looking for a function $\displaystyle B_\mu$ such that:
$\displaystyle B_\mu \simeq \int_a^b e^{ - \frac{(x-\mu)^2}{2\sigma^2} } dx = A_\mu$

Any ideas?

2. ## Re: Approximation of gaussian normalization factor

The normalisation facrtor can quickly be written in terms of the standard normal CDF. (im not sure, but from your post it looks like you might already have worked that out).

Numerical approximations to the CDF are available, eg:
Normal distribution - Wikipedia, the free encyclopedia