Nice explanation, Magnus. Thank you. On Fri, Feb 12, 2021, 9:33 AM Magnus Danielson <[email protected]> wrote:
> Hi, > > On 2021-02-12 12:25, Simon Lewis wrote: > > Hi everyone, > > > > Novice question, but does the 1-sigma, 2-sigma, 3-sigma (68-95-99) rule > > apply to Allan and modified deviations? That is, can I say that that if > my > > MDEV is 1e-11 for 1s, 99% of samples fall within 3 MDEVs? I know that the > > standard variance is the same as the ADEV for white FM, but are the > > coloured components an issue in doing this? > > I think this is a very good question! Quite insightful actually. > > To put it bluntly, no, it's not valid. > > The Allan Deviation just as Standard Deviation is an average of squared > noise, and not average of noise. This changes the distribution from > normal distribution to Chi-square distribution. So, you can not use the > same basic rules. > > To complicate the matter, the Chi-squared distribution depends on the > degrees of freedom you have in the measure. The degrees of freedom > depends on the number of samples you use, but also on other details in > the filtering mechanism, and how that affects the noise, and it turns > out the noise type as in power law slope. So, you can now find > estimators of degrees of freedom for the number of samples and then > different for noise-type. > > So, the confidence interval is set from the type of noise, number of > samples, processing type and the Chi-square scale properties, which will > be asymmetric around the average value compared to the classical normal > distribution. Similar to the classical normal distribution you have the > confidence value for the range, such as 95%. > > The comes the question, how close to the Chi-square does your estimation > of say ADEV or MDEV turn out? Also, be aware, if you have systematic > noise in there, it will not be valid estimation. > > Cheers, > Magnus > > > _______________________________________________ > time-nuts mailing list -- [email protected] > To unsubscribe, go to > http://lists.febo.com/mailman/listinfo/time-nuts_lists.febo.com > and follow the instructions there. > _______________________________________________ time-nuts mailing list -- [email protected] To unsubscribe, go to http://lists.febo.com/mailman/listinfo/time-nuts_lists.febo.com and follow the instructions there.
