Re: Generating "independent" random numbers

[Keith Wright]

From: Zelphir Kaltstahl <zelphirkaltstahl@posteo.de>

> my goal is normal distributed floats (leaving aside the finite
> nature of the computer and floats).

Warning: I am out of my depth, I can't even spell statisticion, but...

The following is either provably correct up to round-off,
or totally stupid.

First define the cumulative distribution for the normal distribution:

$$f(x)= \frac{1}{\sqrt{\pi}} \int_{-\infty}^{x} e^{-x^2/2} dx $$

Now to get a normal random variable, let $u$ be a uniform random number
on [0,1), then $f^{-1}(u)$ is a standard normal random variable.

Computing the inverse of the cumulative normal distribution is left as
an exercise, because I don't know how, but it seems possible.

From: Maxime Devos <maximedevos@telenet.be>

> So, to generate an (approximately) uniform random number on [0,1), you 
> can simply do
>
> (define (random-real)
>     (exact->inexact (/ (random N) N)))
>
> for a suitably large choice of integer N>0.

A choice that makes this nice (on a 32 bit machine) is $N = 2^{32}$.

   -- Keith