This is one implementation for the normal CDF, in terms of the error
function provided in ocamlgsl:

let normal_cdf ~mu ~sigma x =
  (1.0 +. Gsl_sf.erf ((x -. mu) /. (sigma *. sqrt 2.0))) /. 2.0

As Christophe mentioned, this CDF gives you the probability that your random
variable is at most x (rather than greater than x). GSL and ocamlgsl also
provide many other functions related to the normal and other distributions.

On Fri, Apr 15, 2011 at 6:39 AM, Christophe Raffalli <craff73@gmail.com>wrote:

>  Le 15/04/11 11:22, Miguel Pignatelli a écrit :
>
> Hi all,
>
> Maybe this is a long shot, but...
>
> I have a gaussian (normal) distribution defined by its mean and std
> deviation and I want to know the probability of a given known point in the
> curve.
>
> Probability of one point for a continuous law is zero ... You probably wand
> the
> probability Phi(x) of a point in ]-infinity,x] from which you can compute
> the probability of
> a point in any interval ...
>
>
>  I have followed the formula given in [1] but I realized that there are
> cases where P > 1. After struggling myself for a while I realized that that
> formula expresses the probability *density* distribution that happens that
> can be > 1. Are you aware of any module in ocaml to calculate the
> probability [0<P<1]?
>
> (other kind of relevant references are also welcome)
>
> Thanks in advance,
>
> M;
>
> [1] http://en.wikipedia.org/wiki/Normal_distribution
>
>
> The same page has a section :
> Numerical approximations for the normal CDF to compute Phi(x) yourself
> (this is not completely trivial).
>
> Hope this helps,
> Christophe
>
>