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Experimental sampling distributions and confidence intervals of the Allan variance in some DC electrical measurements

The Allan variance is used to characterize stochastic serial correlations in DC electrical measurements when using instruments such as nanovoltmeters and Zener voltage standards. For such applications, it is important to be able to specify the confidence intervals for the estimated Allan variances. By repeating sets of 4096 or 8192 observations 600 times or more in succession, the experimental sampling distribution of the Allan variance is obtained and found to agree well with the chi-square distribution calculated from the number of degrees of freedom estimated from the data. An expression is obtained for approximating the number of degrees of freedom as a function of sampling time; this can then be used to estimate confidence intervals.