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.
