diff --git a/doc/recipe/preprocessor.rst b/doc/recipe/preprocessor.rst
index 92bd400e61..37b1f8675b 100644
--- a/doc/recipe/preprocessor.rst
+++ b/doc/recipe/preprocessor.rst
@@ -2733,8 +2733,8 @@ recipe:
   .. math::
 
     W_1 = \min_{\gamma \in \mathbb{R}^{n \times n}_{+}} \sum_{i,j}^{n}
-    \gamma_{ij} \lvert X_i - R_i \rvert \\
-    \textrm{with} ~~ \gamma 1 = p_X(X);~ \gamma^T 1 = p_R(R)
+    \gamma_{ij} \lvert X_i - R_i \rvert \\ \textrm{with} ~~ \sum_{j}^{n}
+    \gamma_{ij} = p_X(X_i);~ \sum_{i}^{n} \gamma_{ij} = p_R(R_j)
 
   * ``'weighted_emd'``: `Weighted Earth mover's distance`_.
     Similar to the unweighted EMD (see above), but here weights are considered
@@ -2750,6 +2750,9 @@ recipe:
   or `p`\ :sub:`R`\ (`R`\ :sub:`i`) and a number of bins `n` (see the argument
   ``n_bins`` below) that has been derived for the variables `x` and `r` through
   binning.
+  The bins range from the minimum to the maximum value calculated over both the
+  variable of interest and the reference; thus, `X`\ :sub:`i` = `R`\ :sub:`i`)
+  for all `i`.
   `w`\ :sub:`i` are weights that sum to one (see note below) and `N` is the
   total number of samples.