can the normal distribution be integrated?

One time I was writing a program for which I needed to plug in the area under the normal distribution. So I tried to "integrate" it to come up with an equation I could plug numbers into to get this area over certain intervals.


But I couldn't integrate it. Not that I would be the one to find it, but is there such an equation?


I suspect that Paul or Renaud could lead us toward the right tool.


lEroy

Very simple to do actually... excel can do it. Just use the 'normdist' or 'normsdist' function.

But there are very simple and accurate approximations - see Numerical Recipes (available on the web).

Numerical recipes site:


http://www.nr.com/


Error function code:


http://www.ulib.org/webRoot/Books/Numerical_Recipes/bookcpdf/c6-2.pdf


You need to make a change of variable to convert the error function into the normal distribution.

I find it really hard to believe that you do not know how to find how to integrate against a normal distribution. Elroy, for all of your talk do you know the definition of a probability density function?


the integral from negative infinity to t of f(x) times e to the -x squared normalized by 2 pi.