I'm looking for a random number generator which generates random numbers with a
bell curve distribution. For example, if I gave the RNG a range of 0-100, the
most numbers generated near 50. If I gave a range of -4 to +4, then most
numbers would be generated near 0.

Pascal preferred, but other languages ok.
Thanks.

--
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Hi Chuck!

just a quick idea:

function myrandom(max: integer) : integer;
begin
  myrandom := trunc((random + random) * (max+1) / 2.0 )
  { not 2 * random :-)) }
end;

for range 0..100 use myrandom(100);
to achieve a range of -4 to 4 for example use 'r := myrandom(8) - 4;'

i'm really not sure, if this function will result in the distribution
you're looking for.

kind regards
jochen

Maybe you mean a Gauss-function? In that case, you should download
a bunch of SWAG-files from (for example) ftp://garbo.uwasa.fi/pc/turbopas
and search for 'gauss'.

Hope that will help

JRS:  In article <bebt88$3blb...@ID-185685.news.dfncis.de>, seen in
news:comp.lang.pascal.misc, Chuck S. <ch...@gil.net> posted at Mon, 7
Jul 2003 13:40:25 :-

 <URL:http://www.merlyn.demon.co.uk/pas-rand.htm#RandDist>

--
 ? John Stockton, Surrey, UK.  ?...@merlyn.demon.co.uk   Turnpike v4.00   MIME. ?
  <URL:http://www.merlyn.demon.co.uk/> TP/BP/Delphi/&c., FAQqy topics & links;
  <URL:http://www.merlyn.demon.co.uk/clpb-faq.txt>   RAH Prins : c.l.p.b mFAQ;
  <URL:ftp://garbo.uwasa.fi/pc/link/tsfaqp.zip> Timo Salmi's Turbo Pascal FAQ.

On Mon, 7 Jul 2003 20:43:05 +0100, Dr John Stockton

Just for fun (and to learn something), I read John Stockton's web
page, above, and saw my version of Gauss discussed.  Of course,
there's also the simple-minded approximation from the "Mean tends to a
Gaussian" -- simply add up 12 uniformly-distributed random numbers,
which will be approximately a Gaussian with a mean of 6 and a standard
deviation of [here I forget the details, but it is fairly simple to
derive].  I learned this one years ago from the IBM Scientific
Subroutine Package, written in Fortran II (not IV!).

Bob Schor
Pascal Enthusiast

function ZufallNormal (Mittel, SigmaSqr : double) : double;

begin
    ZufallNormal := sqrt(-2 * ln(random)) * sin(2 * pi * random) *
SigmaSqr + Mittel;
end;

On 7 Jul 2003 13:40:25 GMT, "Chuck S." <ch...@gil.net> wrote:

tFloat is whatever floating point type you want.  Give it the mean and
standard deviation you want.  rNormal returns the result.  rNormal2
returns two of them in less time than 2 calls to rNormal.

function rNormal( const mean, sd : tFloat) : tFloat;

{ Returns a FP number that is normal with the given mean   }
{ and standard deviation.  Based on the method of G. E. P. }
{ Box, M. E. Muller, and G. Marsaglia in D. E. Knuth, The  }
{ Art of Computer Programming, Volume 2, 3rd ed., pg. 122  }
{ By Jud McCranie, Dec 2, 1986. Slightly revised 5/30/99, 7/14/00  }

{ if execution time is a consideration, it can be modified
  to return two variables with each call.  See rNormal2 }

var u1, u2, v1, v2, s : tFloat;

begin { --- rNormal --- }

repeat
  u1 := random;
  u2 := random;
  v1 := 2.0 * u1 - 1.0;
  v2 := 2.0 * u2 - 1.0;
  s  := sqr( v1) + sqr( v2);
until s < 1.0;

rNormal := mean + sd * sqrt( (-2.0 * ln( s) / s)) * v2;

end; { --- r normal --- }

procedure rNormal2( const mean, sd : tFloat;
                    out   x1, x2   : tFloat);

{ Returns reals X1 and X2 that are normally distributed with      }
{ the given mean and standard deviation.  Based on the method     }
{ of G. E. P. Box, M. E. Muller, and G. Marsaglia in D. E. Knuth, }
{ The Art of Computer Programming, Volume 2, 3rd ed., pg. 122     }
{ By Jud McCranie, Dec 2, 1986. Slightly revised 5/31/99, 7/14/00 }

var u1, u2, v1, v2, s, thing : tFloat;

begin { --- rNormal2 --- }

repeat
  u1 := random;
  u2 := random;
  v1 := 2.0 * u1 - 1.0;
  v2 := 2.0 * u2 - 1.0;
  s  := sqr( v1) + sqr( v2);
until s < 1.0;

thing := sqrt( (-2.0 * ln( s)) / s);
x1    := mean + sd * v1 * thing;
x2    := mean + sd * v2 * thing;

end; { --- r normal2 --- }