Editing Allan variance (section)

===''B''<sub>3</sub> bias function===
The ''B''<sub>3</sub> bias function relates the 2-sample variance for sample time ''MT''<sub>0</sub> and observation time ''Mτ''<sub>0</sub> with the 2-sample variance (Allan variance) and is defined<ref name=NISTTN1318>J. A. Barnes, D. W. Allan: [http://tf.boulder.nist.gov/general/pdf/878.pdf ''Variances Based on Data with Dead Time Between the Measurements''], NIST Technical Note 1318, 1990.</ref> as

:<math>B_3(N, M, r, \mu) = \frac{\left\langle\sigma_y^2(N, M, T, \tau)\right\rangle}{\left\langle\sigma_y^2(N, T, \tau)\right\rangle},</math>

where
:<math>T = M T_0,</math>
:<math>\tau = M \tau_0.</math>

The ''B''<sub>3</sub> bias function is useful to adjust non-overlapping and overlapping variable ''τ'' estimator values based on dead-time measurements of observation time ''τ''<sub>0</sub> and time between observations ''T''<sub>0</sub> to normal dead-time estimates.

The bias function becomes after analysis (for the ''N''&nbsp;=&nbsp;2 case)

: <math>B_3(2, M, r, \mu) = \frac{2M + MF(Mr) - \sum_{n=1}^{M-1} (M - n) \left[ 2F(nr) - F\big((M + n)r\big) + F\big((M - n)r\big) \right]}{M^{\mu+2} [F(r) + 2]},</math>

where

: <math>F(A) = 2A^{\mu+2} - (A + 1)^{\mu+2} - |A - 1|^{\mu+2}.</math>