This is one implementation for the normal CDF, in terms of the error function provided in ocamlgsl:<div><br></div><div>let normal_cdf ~mu ~sigma x =</div><div>  (1.0 +. Gsl_sf.erf ((x -. mu) /. (sigma *. sqrt 2.0))) /. 2.0</div>

<div><br></div><div>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.</div>

<meta http-equiv="content-type" content="text/html; charset=utf-8"><div><br></div><div><div class="gmail_quote">On Fri, Apr 15, 2011 at 6:39 AM, Christophe Raffalli <span dir="ltr">&lt;<a href="mailto:craff73@gmail.com">craff73@gmail.com</a>&gt;</span> wrote:<br>

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  <div bgcolor="#ffffff" text="#000000">
    Le 15/04/11 11:22, Miguel Pignatelli a écrit :
    <div class="im"><blockquote type="cite">Hi all,
      <br>
      <br>
      Maybe this is a long shot, but...
      <br>
      <br>
      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.</blockquote></div>
    Probability of one point for a continuous law is zero ... You
    probably wand the<br>
    probability Phi(x) of a point in ]-infinity,x] from which you can
    compute the probability of<br>
    a point in any interval ...<div class="im"><br>
    <br>
    <blockquote type="cite"> I have
      followed the formula given in [1] but I realized that there are
      cases where P &gt; 1. After struggling myself for a while I
      realized that that formula expresses the probability *density*
      distribution that happens that can be &gt; 1. Are you aware of any
      module in ocaml to calculate the probability [0&lt;P&lt;1]?
      <br>
      <br>
      (other kind of relevant references are also welcome)
      <br>
      <br>
      Thanks in advance,
      <br>
      <br>
      M;
      <br>
      <br>
      [1] <a href="http://en.wikipedia.org/wiki/Normal_distribution" target="_blank">http://en.wikipedia.org/wiki/Normal_distribution</a>
      <br>
    </blockquote>
    <br></div>
    The same page has a section :<br>
    <h2><span>Numerical
        approximations for the normal CDF</span></h2>
    to compute Phi(x) yourself (this is not completely trivial).<br>
    <br>
    Hope this helps,<br>
    Christophe<br>
    <br>
  </div>

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