Re: Normal distribution random numbers

[Mikael Djurfeldt]

Yes

Den tors 4 juni 2020 17:08Zelphir Kaltstahl <zelphirkaltstahl@posteo.de>
skrev:

> 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>
> 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
>> >
>> >
>>
>>