BUG: min/max on empty categorical fails

doc/source/whatsnew/v1.0.0.rst

@@ -667,6 +667,7 @@ Categorical
   same type as if one used the :meth:`.str.` / :meth:`.dt.` on a :class:`Series` of that type. E.g. when accessing :meth:`Series.dt.tz_localize` on a
   :class:`Categorical` with duplicate entries, the accessor was skipping duplicates (:issue:`27952`)
 - Bug in :meth:`DataFrame.replace` and :meth:`Series.replace` that would give incorrect results on categorical data (:issue:`26988`)
+- Bug where calling :meth:`Categorical.min` or :meth:`Categorical.max` on an empty Categorical would raise a numpy exception (:issue:`30227`)
 
 
 Datetimelike

pandas/core/arrays/categorical.py

@@ -39,7 +39,7 @@
 from pandas.core.dtypes.dtypes import CategoricalDtype
 from pandas.core.dtypes.generic import ABCIndexClass, ABCSeries
 from pandas.core.dtypes.inference import is_hashable
-from pandas.core.dtypes.missing import isna, notna
+from pandas.core.dtypes.missing import isna, na_value_for_dtype, notna
 
 from pandas._typing import ArrayLike, Dtype, Ordered
 from pandas.core import ops
@@ -2116,6 +2116,10 @@ def min(self, skipna=True):
 
         Only ordered `Categoricals` have a minimum!
 
+        .. versionchanged:: 1.0.0
+
+           Returns an NA value on empty arrays
+
         Raises
         ------
         TypeError
@@ -2126,6 +2130,10 @@ def min(self, skipna=True):
         min : the minimum of this `Categorical`
         """
         self.check_for_ordered("min")
+
+        if not len(self._codes):
+            return na_value_for_dtype(self.dtype)
+
         good = self._codes != -1
         if not good.all():
             if skipna:
@@ -2143,6 +2151,10 @@ def max(self, skipna=True):
 
         Only ordered `Categoricals` have a maximum!
 
+        .. versionchanged:: 1.0.0
+
+           Returns an NA value on empty arrays
+
         Raises
         ------
         TypeError
@@ -2153,6 +2165,10 @@ def max(self, skipna=True):
         max : the maximum of this `Categorical`
         """
         self.check_for_ordered("max")
+
+        if not len(self._codes):
+            return na_value_for_dtype(self.dtype)
+
         good = self._codes != -1
         if not good.all():
             if skipna:

pandas/tests/arrays/categorical/test_analytics.py

@@ -35,6 +35,16 @@ def test_min_max(self):
         assert _min == "d"
         assert _max == "a"
 
+    def test_min_max_empty(self):
+        # GH 30227
+        cat = Categorical([], categories=list("ABC"), ordered=True)
+
+        result = cat.min()
+        assert isinstance(result, float) and np.isnan(result)
+
+        result = cat.max()
+        assert isinstance(result, float) and np.isnan(result)
+
     @pytest.mark.parametrize("skipna", [True, False])
     def test_min_max_with_nan(self, skipna):
         # GH 25303