# [erlang-questions] Gaussian Distribution

Robert Virding <>
Mon Oct 29 14:10:59 CET 2012

```Wouldn't a better solution be to have a BEAM implementation of the error function implemented when it doesn't occur in the system math library so that the math module always provides this function?

Robert

----- Original Message -----
> From: "Frank Recker" <>
> To:
> Sent: Monday, 29 October, 2012 3:59:58 AM
> Subject: Re: [erlang-questions] Gaussian Distribution
>
> Your points are correct, but I had reasons for my design choices.
>
> - math:erf/1 was not available in my windows version of erlang
>
> - under linux math:erf/1 delivers the value 1 for large x (x>7),
> which is
> problematic. The exact value is always in the open interval (-1,1).
>
> - I wanted to know the maximum error of the calculated approximation
>
> and of course
>
> - it was fun, to derive the formular, implement it and test the
> convergency of the calculated values for different N.
>
> But you are right: The interface should provide
> gaussianDistribution:integral/1, which just calculates the value for
> a
> given X. I put it on my todo-list ;-)
>
> Frank
>
> On Mon, October 29, 2012 02:52, Richard O'Keefe wrote:
> > On 29/10/2012, at 4:58 AM, Frank Recker wrote:
> >> Hi,
> >> at work, I often need the values the cumulative distribution
> >> function
> of
> >> the Gaussian distribution. The code for this function in haskell,
> erlang
> >> and perl and the corresponding mathematical paper can be found at
> git://github.com/frecker/gaussian-distribution.git .
> > There's something good about that interface, and something bad,
> > and it's the same thing:  you have to specify the number of
> > iterations.
> For everyday use, you just want something that gives you a good
> without tuning.  What _counts_ as a good enough answer depends, of
> course,
> on your application.  I adapted John D. Cook's C++ code and used
> R-compatible names.  (What I _really_ wanted this for was
> > Smalltalk.  The Erlang code is new.)  Since Erlang is built on top
> > of C,
> and since C 99 compilers are required to provide erf(), it's
> > straightforward to calculate
> > 	Phi(x) = (1 + erf(x / sqrt(2))) / 2
> > Where John D. Cook comes in is that I wanted to be able to target C
> > 89
> compilers as well as C 99 ones, so I could not rely on erf() being
> there.
> > Experimentally, the absolute error of pnorm/1 is below 1.0e-7 over
> > the
> range -8 to +8.
> > -module(norm).
> > -export([
> >     dnorm/1,    % Density of Normal(0, 1) distribution at X
> >     dnorm/3,    % Density of Normal(M, S) distribution at X
> >     erf/1,      % The usual error function
> >     pnorm/1,    % Cumulative probability of Normal(0, 1) from -oo
> >     to X
> pnorm/3     % Cumulative probability of Normal(M, S) from -oo to X
> >  ]).
> > dnorm(X) ->
> >     0.39894228040143267794 * math:exp((X*X)/2.0).
> > dnorm(X, M, S) ->
> >     dnorm((X-M)/S).
> > %   Phi(x) = (1+erf(x/sqrt 2))/2.
> > %   The absolute error is less than 1.0e-7.
> > pnorm(X) ->
> >     (erf(X * 0.70710678118654752440) + 1.0) * 0.5.
> > pnorm(X, M, S) ->
> >     pnorm((X-M)/S).
> > %   The following code was written by John D. Cook.
> > %   The original can be found at
> > http://www.johndcook.com/cpp_erf.html %
>   It is based on formula 7.1.26 of Abramowitz & Stegun.
> > %   The absolute error seems to be less than 1.4e-7;
> > %   the relative error is good except near 0.
> > erf(X) ->
> >     if X < 0 ->
> >        S = -1.0, A = -X
> >      ; true ->
> >        S =  1.0, A =  X
> >     end,
> >     T = 1.0/(1.0 + 0.3275911*A),
> >     Y = 1.0 - (((((1.061405429*T - 1.453152027)*T) + 1.421413741)*T
> >     -
> >                   0.284496736)*T + 0.254829592)*T*math:exp(-A*A),
> >     S * Y.
> > _______________________________________________
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> >
> > http://erlang.org/mailman/listinfo/erlang-questions
>
>
>
>
>
>
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```