diff --git a/sklearn/metrics/_regression.py b/sklearn/metrics/_regression.py
index 9be9f1d954fcc..31c2e0bddaa90 100644
--- a/sklearn/metrics/_regression.py
+++ b/sklearn/metrics/_regression.py
@@ -1750,7 +1750,12 @@ def d2_pinball_score(
     This metric is not well-defined for a single point and will return a NaN
     value if n_samples is less than two.
 
-     References
+    This metric is not a built-in scoring string for use in model selection
+    tools such as `GridSearchCV` or `RandomizedSearchCV`.
+    To use it as a custom scoring function, wrap it using
+    :func:`~sklearn.metrics.make_scorer`. See Examples for details.
+
+    References
     ----------
     .. [1] Eq. (7) of `Koenker, Roger; Machado, José A. F. (1999).
            "Goodness of Fit and Related Inference Processes for Quantile Regression"
@@ -1761,18 +1766,30 @@ def d2_pinball_score(
 
     Examples
     --------
+    >>> import numpy as np
     >>> from sklearn.metrics import d2_pinball_score
-    >>> y_true = [1, 2, 3]
-    >>> y_pred = [1, 3, 3]
-    >>> d2_pinball_score(y_true, y_pred)
-    0.5
-    >>> d2_pinball_score(y_true, y_pred, alpha=0.9)
-    0.772...
-    >>> d2_pinball_score(y_true, y_pred, alpha=0.1)
-    -1.045...
-    >>> d2_pinball_score(y_true, y_true, alpha=0.1)
-    1.0
+    >>> y_true = [3, -0.5, 2, 7]
+    >>> y_pred = [2.5, 0.0, 2, 8]
+    >>> d2_pinball_score(y_true, y_pred, alpha=0.95)
+    0.968...
+
+    Using with :func:`~sklearn.metrics.make_scorer`:
+
+    >>> from sklearn.metrics import make_scorer, d2_pinball_score
+    >>> pinball_95_scorer = make_scorer(d2_pinball_score, alpha=0.95)
+    >>> from sklearn.model_selection import GridSearchCV
+    >>> from sklearn.linear_model import LinearRegression
+    >>> X = np.array([[1], [2], [3], [4]])
+    >>> y = np.array([2.5, 0.0, 2, 8])
+    >>> grid = GridSearchCV(
+    ...     LinearRegression(),
+    ...     param_grid={"fit_intercept": [True, False]},
+    ...     scoring=pinball_95_scorer,
+    ...     cv=2,
+    ... )
+    >>> _ = grid.fit(X, y)
     """
+
     y_type, y_true, y_pred, multioutput = _check_reg_targets(
         y_true, y_pred, multioutput
     )