and ξ can be computed by replacing the computed power allocation (18) in the third line of (17) [16], namely, 1 NT ∑ k = 0 M − 1 log 2 1 + P a k ξ γ k β = R. (20).
For large samples, the p-value can be computed by replacing the unknown correlation by the sample correlation, and the resulting test is quite satisfactory.
Following the arguments leading to Eq. (17), the drift ratio can now be computed by replacing (K_{i} h_{i}^{2} (1 + bar{K}_{D,i} )) with αK D,i and inserting K C = 0 in Eq. (17).
If all errors are below certain tolerances, the process is finished, otherwise go to step 3. Projected solutions are computed by replacing obtained solutions for each pair of variables in the general flow equation (9).
Then, the estimated Wiener mask is computed by replacing s j (f,t) by ŝ j ( t, f ) at Equation 23 as follows: α ̂ j ′ ( t, f ) = m i, j ′ 2 ŝ j ′ ( f, t ) 2 ∑ j m i, j 2 ŝ j ( f, t ) 2. (2.).
The empirical P-value of Tloss(X) is computed by replacing 'gain' with 'loss' and reversing the inequality in Step 4. Both definitions yield P-values that are easy to interpret and are automatically adjusted for multiple comparisons across the markers.
As an advantage, the distribution of the structural variable(s) is computed by means of non-parametric techniques, which replace the fit of parametric distributions, an awkward task involving arbitrary choices.
The normalizing factor may be easily computed by replacing xt by its actual value in (22).
The filtered (standard deviation) image is then normalized (via pixel wise division) by the mean image, which is also computed by replacing each pixel by the mean value of pixels in a local window around the pixel.
A modified distance matrix was then computed by replacing each l i, j with a uniform draw from the interval [0.75 l i, j, 1.25 l i, j], and a modified tree was computed using Unweighted Pair Group Method with Arithmetic Mean (UPGMA) on the modified distance matrix.
The correlation C n between secular variation models can be computed in the same way by just replacing the Gauss coefficients by their first time derivatives where we adopted the "dot" notation for time derivatives.
