[erlang-questions] Gaussian Distribution

Björn-Egil Dahlberg <>
Mon Oct 29 12:34:43 CET 2012

```Do we lack a proper statistics library in erlang?

If so, should we add one to stdlib? or should it be a standalone app?

I realize that there are already a couple out there, for example
basho_stats but perhaps we need a unified one. One that is a lib and not
a process framework.

I began some thoughts for a statistics lib at
https://github.com/psyeugenic/matstat

I added what I usually need when doing measurements and looked at what
other languages/runtimes has implemented but back to the question. Do we
lack a library and should we organize us to begin constructing one together?

// Björn-Egil

On 2012-10-29 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 .
> 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 answer
> 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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>

```