home/regression-approach.md

@@ -7,6 +7,7 @@ title: regression approach - powerlaw
 
 
 
+
 ## Dependency
 
 It is assumed the data can be described by a power law, expressed either as Y or X dependent (referring to the second and first axis on a fatigue curve).
@@ -97,11 +98,8 @@ E = Y_{\textrm{p}} - Y_{\textrm{d}}
 
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 <div align="center">
-![subset_error_band](uploads/b35fa634cc7dc99f39255bca21e6fa5c/subset_error_band.png){width=25%}
-</div>
-
-<div align="center">
-![quantile_exmaple_error](uploads/f6950315da8dfc9c3d3054c0dfd95cb5/quantile_exmaple_error.png){width=25%}
+![subset_error_band](uploads/b35fa634cc7dc99f39255bca21e6fa5c/subset_error_band.png){width=35%}&nbsp;&nbsp;
+![quantile_exmaple_error](uploads/f6950315da8dfc9c3d3054c0dfd95cb5/quantile_exmaple_error.png){width=35%}
 </div>
 
 Extract the data with a positive error. We are only interested in the positive difference, as these are an indication of the points below the mean line.
@@ -112,6 +110,9 @@ E = E\left[E > 0\right], \quad X_{s} = X_{s}[E>0], \quad Y_{s} = Y_{s}[E>0]
 
 Sort the data based on the error
  
+```math
+E = E\left[\textrm{argsort}\left(E\right)\right], \quad X_{s} = X_{s}[\textrm{argsort}\left(E\right)\right], \quad Y_{s} = Y_{s}[\textrm{argsort}\left(E\right)\right]
+```
 
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