BUG: Some `Index` reductions fail with `string[pyarrow]`

[jrbourbeau]

Pandas version checks

• I have checked that this issue has not already been reported.

• I have confirmed this bug exists on the latest version of pandas.

• I have confirmed this bug exists on the main branch of pandas.

Reproducible Example

import pandas as pd

x = pd.Index(['a', 'b', 'a'], dtype=object)
print(f"{x.min() = }")  # This works

y = pd.Index(['a', 'b', 'a'], dtype="string[python]")
print(f"{y.min() = }")  # This works

z = pd.Index(['a', 'b', 'a'], dtype="string[pyarrow]")
print(f"{z.min() = }")  # This errors

Issue Description

When an Index with string[pyarrow] data contains repeated data, for example pd.Index(['a', 'b', 'a'], dtype="string[pyarrow]"), .min() / .max() fail.

The above code snippet fails with

Traceback (most recent call last):
  File "/Users/james/projects/dask/dask/string-min.py", line 11, in <module>
    print(f"{z.min() = }")
  File "/Users/james/mambaforge/envs/dask-py39/lib/python3.9/site-packages/pandas/core/indexes/base.py", line 7225, in min
    return self._values.min(skipna=skipna)  # type: ignore[attr-defined]
AttributeError: 'ArrowStringArray' object has no attribute 'min'

Expected Behavior

I'd expect using string[pyarrow] data to return the same result as object and string[python].

cc @phofl @mroeschke

Installed Versions

INSTALLED VERSIONS
------------------
commit           : 8dab54d6573f7186ff0c3b6364d5e4dd635ff3e7
python           : 3.9.15.final.0
python-bits      : 64
OS               : Darwin
OS-release       : 22.2.0
Version          : Darwin Kernel Version 22.2.0: Fri Nov 11 02:08:47 PST 2022; root:xnu-8792.61.2~4/RELEASE_X86_64
machine          : x86_64
processor        : i386
byteorder        : little
LC_ALL           : None
LANG             : en_US.UTF-8
LOCALE           : en_US.UTF-8

pandas           : 1.5.2
numpy            : 1.24.0
pytz             : 2022.6
dateutil         : 2.8.2
setuptools       : 59.8.0
pip              : 22.3.1
Cython           : None
pytest           : 7.2.0
hypothesis       : None
sphinx           : 4.5.0
blosc            : None
feather          : None
xlsxwriter       : None
lxml.etree       : None
html5lib         : 1.1
pymysql          : None
psycopg2         : None
jinja2           : 3.1.2
IPython          : 8.7.0
pandas_datareader: None
bs4              : 4.11.1
bottleneck       : None
brotli           :
fastparquet      : 2023.1.0
fsspec           : 2022.11.0
gcsfs            : None
matplotlib       : 3.6.2
numba            : None
numexpr          : 2.8.3
odfpy            : None
openpyxl         : None
pandas_gbq       : None
pyarrow          : 10.0.1
pyreadstat       : None
pyxlsb           : None
s3fs             : 2022.11.0
scipy            : 1.9.3
snappy           :
sqlalchemy       : 1.4.46
tables           : 3.7.0
tabulate         : None
xarray           : 2022.9.0
xlrd             : None
xlwt             : None
zstandard        : None
tzdata           : None

[jrbourbeau]

Hmm, actually this may be more generic than when there's repeated data. I just stumbled across this case where there aren't any repeated items in the index

In [1]: import pandas as pd

In [2]: x = pd.Index(['k', 'l', 'i'], dtype='string[python]')

In [3]: x.min()
Out[3]: 'i'

In [4]: x = pd.Index(['k', 'l', 'i'], dtype='string[pyarrow]')

In [5]: x.min()
---------------------------------------------------------------------------
AttributeError                            Traceback (most recent call last)
Cell In[5], line 1
----> 1 x.min()

File ~/mambaforge/envs/dask-py39/lib/python3.9/site-packages/pandas/core/indexes/base.py:7225, in Index.min(self, axis, skipna, *args, **kwargs)
   7221         return self._na_value
   7223 if not self._is_multi and not isinstance(self._values, np.ndarray):
   7224     # "ExtensionArray" has no attribute "min"
-> 7225     return self._values.min(skipna=skipna)  # type: ignore[attr-defined]
   7227 return super().min(skipna=skipna)

AttributeError: 'ArrowStringArray' object has no attribute 'min'

[phofl]

Hi, thx for your report. Yep this is a generic problem.

If you have this in a Series, then we are accessing reduction functions through _reduce while the index class calls them directly, which raises the error.