>You're done

Yes, and everyone will be doing it slightly differently, and the
sampling from this curve will turn out to be just _slightly_ different
from the one implemented in the srfi, which will give a whole lot of
funky debugging techniques to find out where is the problem that the
user would have to learn.

If you're implementing a sampler from a distribution there should be a
way to get _the same_ distribution that is used to provide the
samples, in the sense of (eq?).

On Fri, 17 Jul 2020 at 12:43, Linas Vepstas <xxxxxx@gmail.com> wrote:
>
>
>
> On Thu, Jul 16, 2020 at 10:53 PM Vladimir Nikishkin <xxxxxx@gmail.com> wrote:
>>
>>
>> It's just strange to see a library providing a "normally-distributed
>> random number" generator, but not an actual function to compute the
>> value of a gaussian bell in, i.g. that particular points where the
>> generator has produced some samples. An inverse value is extremely
>> often needed in statistical analysis.
>
>
> But this is almost trivial for the gaussian:
>
> (define mean (fold + 0 lis))
> (define rms (sqrt (fold (x s) (+ s (* x x))) 0 lis)))
>
> That's it. You're done. That's the gaussian bell.  Did you want the Student t-distribution instead?  If you want to get fancier than that... the standard advice is "use Gnu R" or "use SciPy" but re-imagining either of those two is a whole nuther thing. (There is a Jupyter for scheme, somewhere, but it is not obviously maintained and besides Jupyter is .. problematic for record-keeping and publishing. Lacks long-term stability. Depends on super-messy undebuggable javascript. Cannot be checked into git ... etc. There are several competitors to Jupyter that are more rational, but they are not popular, and do not provide scheme.)
>
>> Furthermore, a normal distribution spans all the real line from -inf
>> to inf.
>
>
> Yes. Although it is impossible to ever produce those values .. values greater than six sigma are exceptionally rare. Assuming you can generate one random value per nanosecond,  you will generate a value greater than +11 or -11 approximately once per age of the universe. (Recall the age of the universe being a mere 4e26 nanoseconds old - a number that easily fits in a single-precision float).
>
>> How does this work with Scheme numbers?
>
>
> single-precision-float is more than good enough for this particular example...
>
> Although I will once again call for a srfi that wraps up either GnuMP or MPFR because some applications (number theory) need more than 56 bits of precision. More than 600 decimal places is very common.
>
> > I think it is not what I find aesthetically pleasing
>
> Aesthetics is always important, but I cannot guess at the sense of aesthetics at play, here... ?
>
> -- linas

--
Yours sincerely, Vladimir Nikishkin