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From: Rune Allnor on 31 Jan 2010 03:14
On 31 Jan, 09:06, "Muhammad Farrukh Yaqub" <farrukh.ya...(a)gmail.com>
wrote:
> Hi Everyone,
>
> I'm calculating higher order Cumulants (order>2) for Gaussian Distribution. Theoretically these Cumulants should be equal to zero. But I'm not getting these Cumulants equal to zero.

That's because you don't compute the *true* cumulants of
a 'truly' Gaussian sequence, but merely *estimates* of the
cumulants in a limited sample of a near-Gaussian process.

Rune
From: Muhammad Farrukh Yaqub on 31 Jan 2010 03:49
Hi Rune,

Thank you very much for highlighting the problem. Could you please advise me, to maintain a good level of accuracy, what should be the size of the 'window of random variable (Gaussian in our discussion)' and how many iterations should I go for to have the averaging effect. Of course we can't make them too high to limit the delays.

Thanking you in anticipation.

Regards,

Farrukh

Rune Allnor <allnor(a)tele.ntnu.no> wrote in message <44ab4048-b455-49a8-b83e-dd7588750b44(a)a5g2000yqi.googlegroups.com>...
> On 31 Jan, 09:06, "Muhammad Farrukh Yaqub" <farrukh.ya...(a)gmail.com>
> wrote:
> > Hi Everyone,
> >
> > I'm calculating higher order Cumulants (order>2) for Gaussian Distribution. Theoretically these Cumulants should be equal to zero. But I'm not getting these Cumulants equal to zero.
>
> That's because you don't compute the *true* cumulants of
> a 'truly' Gaussian sequence, but merely *estimates* of the
> cumulants in a limited sample of a near-Gaussian process.
>
> Rune
From: Rune Allnor on 31 Jan 2010 05:25
On 31 Jan, 09:49, "Muhammad Farrukh Yaqub" <farrukh.ya...(a)gmail.com>
wrote:
> Hi Rune,
>
> Thank you very much for highlighting the problem. Could you please advise me, to maintain a good level of accuracy, what should be the size of the 'window of random variable (Gaussian in our discussion)' and how many iterations should I go for to have the averaging effect. Of course we can't make them too high to limit the delays.

That's the 'art' part of 'the art of data analysis.'

There are no right or wrong answers to these kinds
of questions, only experiences. Try a few simulations
with a few different conditions, and try and build
intuition yourself.

If you have a good Pseudo Random Number Generator (that
is, a PRNG that emulates the Gaussian distribution well)
one would expect the higher order cumulants to vanish
as the number of data points increases.

Try different sizes and see. Try different PRNGs as well,
to see the differences. Don't be surprised if the higher
order cumulants are used as quality metrics for Gaussian
PRNGs.

Rune
From: Muhammad Farrukh Yaqub on 31 Jan 2010 05:40
Thank you very very much. It's of course a great favor.

Rune, I'm using Matlab built in function, 'randn' to generate the Gaussian Noise. Could you please advise me some better 'Pseudo random number generator' which approximates better to Gaussian Distribution.

Thanking you once again.

Farrukh

Rune Allnor <allnor(a)tele.ntnu.no> wrote in message <a0b0f304-ef07-4dec-8dee-b9cd03b06f5a(a)c29g2000yqd.googlegroups.com>...
> On 31 Jan, 09:49, "Muhammad Farrukh Yaqub" <farrukh.ya...(a)gmail.com>
> wrote:
> > Hi Rune,
> >
> > Thank you very much for highlighting the problem. Could you please advise me, to maintain a good level of accuracy, what should be the size of the 'window of random variable (Gaussian in our discussion)' and how many iterations should I go for to have the averaging effect. Of course we can't make them too high to limit the delays.
>
> That's the 'art' part of 'the art of data analysis.'
>
> There are no right or wrong answers to these kinds
> of questions, only experiences. Try a few simulations
> with a few different conditions, and try and build
> intuition yourself.
>
> If you have a good Pseudo Random Number Generator (that
> is, a PRNG that emulates the Gaussian distribution well)
> one would expect the higher order cumulants to vanish
> as the number of data points increases.
>
> Try different sizes and see. Try different PRNGs as well,
> to see the differences. Don't be surprised if the higher
> order cumulants are used as quality metrics for Gaussian
> PRNGs.
>
> Rune
From: Rune Allnor on 31 Jan 2010 05:54
On 31 Jan, 11:40, "Muhammad Farrukh Yaqub" <farrukh.ya...(a)gmail.com>
wrote:
> Thank you very very much. It's of course a great favor.
>
> Rune, I'm using Matlab built in function, 'randn' to generate the Gaussian Noise. Could you please advise me some better 'Pseudo random number generator' which approximates better to Gaussian Distribution.

Check the docs for RANDN. You might be able to configure the
workings of the PRNG.

Apart from that, I use C++, where the Boost.Random library

http://www.boost.org/doc/libs/1_41_0/libs/random/index.html

offers a quite comprehensive suite of PRNGs.

Rune
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