Magnus Danielson magnus at rubidium.dyndns.org
Sat Oct 27 17:43:33 EDT 2018

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On 10/26/18 1:42 PM, Ole Petter Ronningen wrote:
> Hi, Attila
>
>> I see two issues here: If your random numbers are indeed between 0 and 1,
>> as you write, then they are uniformly distributed, and not normally
>> distributed. This will give you a slight bias when integrating.
>>
>
> 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.

1/sqrt(12) will be the power of uniform distribution so multiply with
sqrt(12) will do the the trick to get standard distribution of 1 from
uniform distribution. It will however not produce normal distribution.

A simple trick to transform uniform distribution to normal distribution
like shape is to take 12 samples and add them together. A special trick
is to take them pair-wise and subtract them and then add 6 differences,
to avoid DC bias of typical uniform distribution generation (as typical
pseudo-noise generators does not have all 0 state in them). The result
of this subtract-add trick is a normal distribution like thing with the
standard distribution of 1. More or fewer sample-pairs can be added if
the product is scaled appropriately.

The Box-Mueller algorithm is another way to convert uniform distribution
to normal distribution.

However, for ADEV processing, the uniform of normal distribution is not
important to the expected value of ADEV, but to the confidence
intervals. For larger number of samples this becomes less of an issue
and the slopes of the noise dominates.

>> The other issue is the integration itself. Because you do a nummerical
>> integration at discrete time steps, you will get a slight offset.
>>
>
> I suspect the issue may be this - but I do not immediately see how..

See my previous post.

Cheers,
Magnus

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