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Re: Normal distribution random numbers
From: |
Zelphir Kaltstahl |
Subject: |
Re: Normal distribution random numbers |
Date: |
Thu, 4 Jun 2020 17:08:12 +0200 |
User-agent: |
Mozilla/5.0 (X11; Linux x86_64; rv:60.0) Gecko/20100101 Icedove/60.9.0 |
Hi Mikael!
Thanks for putting that into perspective and giving some numbers!
When I looked at the code of Guile for random:normal, I also guessed,
that it makes use of that Box-Muller-transform, but wasn't sure, so
thanks for confirming that as well.
So basically the tails are wrong, but to draw a number in the area where
the tails are wrong is so unlikely, that it would take that much time,
as stated in your number example, if I understand this correctly(?/.)
Regards,
Zelphir
On 04.06.20 17:03, Mikael Djurfeldt wrote:
> Hi Zelphir,
>
> random:normal actually uses the Box-Muller-transform. But since it
> uses 64 bits, we only loose values that would be generated once in
> 2*10^20. That is, if we could draw one billion numbers per second,
> such values would be drawn once in 7000 years. So, we would start
> noticing an anomaly after maybe 100000 years or so.
>
> But maybe we should replace this with some more correct and efficient
> algorithm at some point.
>
> Best regards,
> Mikael
>
> Den lör 30 maj 2020 22:43Zelphir Kaltstahl <zelphirkaltstahl@posteo.de
> <mailto:zelphirkaltstahl@posteo.de>> skrev:
>
> 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
> >
> >
>