Re: Normal distribution random numbers

[Zelphir Kaltstahl <zelphirkaltstahl@posteo.de>]

I just realized, that I did not check what Guile implements as
non-SRFIs. I found:
https://www.gnu.org/software/guile/manual/html_node/Random.html which
has `random:normal`! I should have checked that first. Still good to
know, what a can of worms normal distribution implementation can be.

On 30.05.20 22:21, Zelphir Kaltstahl wrote:
> Hi Guile Users!
>
> I recently wrote a little program involving lots of uniformly
> distributed random integers. For that I used SRFI-27 and it works fine.
>
> Then I thought: How would I get normal distributed random numbers? I
> don't have a project or program in mind for this, but it struck me, that
> I do not know, how to get a normal distribution from a uniform
> distribution. So I dug into the matter …
>
> Turns out the math is not really my friend:
>
> * https://stackoverflow.com/a/3265174 – OK, if that's true, then don't
> use Box-Muller-Transform
> * https://stackoverflow.com/a/86885 – The what? I need to somehow
> inverse the Gaussian distribution to get a function to calculate normal
> distributed values from uniformly distributed values? Something like
> that. Safe to say it is above my current math skills.
> * The wiki page also does not help me much:
> https://en.wikipedia.org/wiki/Inverse_transform_sampling Seems too
> complicated.
>
> So I thought: "OK, maybe I can simply copy, how other languages
> implement it!" The wiki page mentions, that R actually makes use of the
> inverse thingy. So I set out to look at R source code:
>
> * https://github.com/wch/r-source/blob/master/src/nmath/rnorm.c – OK,
> looks simple enough … Lets see what `norm_rand` is …
> * https://github.com/wch/r-source/blob/master/src/nmath/snorm.c#L62 –
> yeah … well … I'm not gonna implement _that_ pile of … Just look at the
> lines
> https://github.com/wch/r-source/blob/master/src/nmath/snorm.c#L135-L196
> what a mess! Not a single comment to help understanding in it. Such a
> disappointment.
> * Python also seems to only use an approximation with magic constants:
> https://github.com/python/cpython/blob/3.8/Lib/random.py#L443
>
> So it seems, that there is no easy way to implement it properly with
> correct tails to the left and right side of the distribution, something
> clean and not made with mathematical traps built-in. Or is there?
>
> I found a post about using 2 normal distributions to do
> Box-Muller-transform:
> https://www.alanzucconi.com/2015/09/16/how-to-sample-from-a-gaussian-distribution/
>
> However, it seems to require a uniform float not integer and it is the
> Box-Muller-transform, which is said to clamp between -6 and 6 according
> to the people writing the answers on stackoverflow.
>
> So my question is: Is there a good implementation in the Guile universe
> already? (Or a simple way to implement it?) I don't really need it right
> now, but I think this thing could be an obstacle for many people without
> serious math knowledge and it would be good to know, where to find it,
> should one have need for normal distributed random numbers.
>
> Regards,
> Zelphir
>
>