Editing Allan variance (section)

===Confidence interval===
The [[confidence interval]] can be established using [[chi-squared distribution]] with df degrees of freedom by using the [[Scaled chi-squared distribution|distribution of the sample variance]]:<ref name=IEEE1139/><ref name=Howe1981>D. A. Howe, D. W. Allan, J. A. Barnes: [http://tf.boulder.nist.gov/general/pdf/554.pdf ''Properties of signal sources and measurement methods''], pages 464–469, Frequency Control Symposium #35, 1981.</ref>

:<math>\chi^2 = \frac{\text{df}\,s^2}{\sigma^2},</math>

where ''s''<sup>''2''</sup> is the sample variance of our estimate, ''σ''<sup>2</sup> is the true variance value, df is the degrees of freedom for the estimator, and ''χ''<sup>2</sup> is calculated based on the inverse cummulative density distribution of a ''χ''<sup>2</sup>  with df degrees of freedom. For a 90% probability, covering the range from the 5% to the 95% range on the probability curve, the upper and lower limits can be found using the inequality

:<math>\chi^2(0.05) \le \frac{\text{df}\,s^2}{\sigma^2} \le \chi^2(0.95),</math>

which after rearrangement for the true variance becomes

:<math>\frac{\text{df}\,s^2}{\chi^2(0.95)} \le \sigma^2 \le \frac{\text{df}\,s^2}{\chi^2(0.05)}.</math>