[erlang-questions] Gaussian Distribution

[Frank Recker]

I think the Gnu Scientific Library (http://www.gnu.org/software/gsl/) has
everything one ever needs. But if you cannot include it (as it is the case
for me) a nativ erlang library would be great.

Frank

On Mon, October 29, 2012 12:34, Björn-Egil Dahlberg wrote:
> 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 .
>> 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 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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>>
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