home/regression-approach.md

@@ -10,6 +10,7 @@ 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).
@@ -123,8 +124,6 @@ E = E\left[:-I_{\alpha}\right],
 \quad X_{s} = X_{s}\left[:-I_{\alpha}\right],
 \quad Y_{s} = Y_{s}\left[:-I_{\alpha}\right]
 ```
-The last entry in the scaled arrays are now the quantile of interest.
-
 **Step 6** <br>
 Renormalize the data.
 
@@ -132,6 +131,12 @@ Renormalize the data.
 X_{\Gamma} = X_s \left(X_{\textrm{d,max}} - X_{\textrm{d,min}}\right) + X_{\textrm{d,min}}, \quad
 Y_{\Gamma} = Y_s \left(Y_{\textrm{d,max}} - Y_{\textrm{d,min}}\right) + Y_{\textrm{d,min}}
 ```
+Where the last entry is the exact quantile of interest 
+
+```math
+X_{\alpha} = X_{\Gamma}[-1], \quad
+Y_{\alpha} = Y_{\Gamma}[-1]
+```
 
 **Step 6** <br>
 Compute the adjustment coefficient associated with the quantile of interest -