# Gaussian pseudo-random numbers -- math issues

rchilderic at free.fr rchilderic at free.fr
Thu Oct 23 01:25:40 CDT 2008

```Selon Mark Smith <lists at futilism.com>:

> Timothy, the only way I could find of doing what you want is called
> 'the polar form of the Box-Muller transformation'.
>
> Fortunately, it's not as bad as it sounds. :)
>
> I've copied an ADA implementation, and here it is:
>
> function polarBoxMuller pLength, pMean, pSdev
>     put false into useLast
>     repeat pLength
>
>        repeat
>           put ((random(101) - 1) * 0.02) - 1 into x1 -- generate a
> random number between -1 and +1
>           put ((random(101) - 1) * 0.02) - 1 into x2
>
>           put (x1 * x1) + (x2 * x2) into w
>           if w <= 1 then exit repeat
>        end repeat
>
>        if w <> 0 then put ln(w) * -2 into w -- rev barfs if w is zero
>        if w <> 0 then put sqrt(w) / w into w -- ditto
>
>        put x1 * w into y1
>        put x2 * w into y2
>
>        put pMean + y1 * pSdev & comma after tList
>        put pMean + y2 * pSdev & comma after tList
>     end repeat
>
>     return char 1 to -2 of tList
> end polarBoxMuller
>
> This should give you a comma delimited list of (fairly) normally
> distributed numbers.
>
> Best,
>
> Mark
>
> ps. I enjoy this sort of thing, so thanks for the question!
>
> On 21 Oct 2008, at 23:03, Timothy Miller wrote:
>
> > Greetings,
> >
> > I'm interested an a modest statistics demonstration, but I can't
> > figure out how do to the math myself.
> >
> > I'd like to have a few lines of code that produces a sequence of
> > numbers. (whole numbers would probably be okay). I'd like to
> > specify the number of numbers generated. Let's call that Z.
> >
> > I'd like also to specify the desired mean and standard deviation.
> > I'd like the function (is this a function??) to work in such a way
> > that if Z is large, the set of numbers generated, if graphed as a
> > frequency distribution, would be normally distributed, i.e., Gaussian.
> >
> > If Z is rather small, then the mean and standard deviation of the
> > numbers produced will would only approximate the desired mean and
> > standard deviation. Different runs would produce different actual
> > means and standard deviations.
> >
> > If Z is very small, like 3 or 4, the numbers will look almost random.
> >
> > I hope I explained that clearly.
> >
> > Optionally, I might also be able to enter a variable that would
> > specify the desired number of digits to the right of the decimal
> > point.
> >
> > No favors are requested. I'd really be rather uncomfortable with a
> > generous gesture. However, if someone has some code like this
> > sitting around, and you're willing to share it, with a few notes
> > about how to use it, I'd appreciate it. If not, it can't be helped.
> >
> > Hmmmm... I wonder if some website somewhere would do the work for
> > me. That could work... I looked around, but didn't find anything.
> >
> >
> > Tim Miller
> >
> >
> >
> >
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```