Ole Petter Ronningen opronningen at gmail.com
Sun Oct 28 03:38:28 EDT 2018

```Hi, Tom!

I have looked at the pages you link to many times, they really are very
good - my goal here was to get down to the nitty-gritty myself, just
understand the details better.

Regarding possible bias in the Excel RNG, this was my first hunch as well,
but when I repeated the experiment with W PM data generated in Stable32 I
got similar results. The box-muller code goes in my toolbox, though! :)

Thanks
Ole

On Fri, Oct 26, 2018 at 9:02 PM Tom Van Baak <tvb at leapsecond.com> wrote:

> Ole,
>
> > I'm simulating some noise to try to improve my somewhat sketchy
> > understanding of what goes on with the various noise types as shown on an
> > ADEV plot. Nothing fancy, ~3600 points of gaussian random numbers
> between 0
> > and 1 in excel, imported into Timelab as phase data, scaled to ns.
>
> I forgot to mention this page where I use Stable32 and TimeLab to look at
> all 5 noise types:
>
>
> > You are correct, my statement was imprecise - I generate numbers between
> 0
> > and 1, but then multiply that with a function in Excel that yields a
> normal
> > distribution with a standard distribution of 1.
>
> If you suspect problems with Excel, perhaps try something in Python or C
> That also will make it possible to work with millions of points when
> necessary.
> For random numbers I use ancient code by George Marsaglia, and also
> Mersenne Twister 19937.
> To convert uniform [0-1] random to Gaussian I use:
>
> // Get normal (Gaussian) random sample with mean 0 and standard deviation 1
> // See https://en.wikipedia.org/wiki/Marsaglia_polar_method
> double normal (void)
> {
>     // Use Box-Muller algorithm
>     double u1 = genrand1();
>     double u2 = genrand1();
>     double r = sqrt(-2.0 * log(u1));
>     double pi = 4 * atan(1);
>     double theta = 2.0 * pi * u2;
>     return r * sin(theta);
> }
>
> /tvb
>
>
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```