[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
> 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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