[erlang-questions] Gaussian Distribution
Mon Oct 29 13:31:55 CET 2012
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.
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
> 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
> // Björn-Egil
> On 2012-10-29 02:52, Richard O'Keefe wrote:
>> On 29/10/2012, at 4:58 AM, Frank Recker wrote:
>>> at work, I often need the values the cumulative distribution function
>>> the Gaussian distribution. The code for this function in haskell,
>>> 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
>> Experimentally, the absolute error of pnorm/1 is below 1.0e-7 over the
>> range -8 to +8.
>> 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) ->
>> % 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) ->
>> % 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
>> 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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