BUG: inconsistent behaviour of the method .idxmin between timedelta datatype & int datatypes

[JasonMendoza2008]

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

incomplete_df: pd.DataFrame = pd.DataFrame({'event1': [pd.Timedelta("1 days"),    pd.Timedelta("2 days"), pd.Timedelta("nat"),    pd.Timedelta("5 days") ,    pd.Timedelta("6 days"), pd.Timedelta("nat"),    pd.Timedelta("nat"),    pd.Timedelta("11 days"),    pd.Timedelta("nat"),    pd.Timedelta("15 days")],   
                              'event2': [pd.Timedelta("nat"),   pd.Timedelta("1 days") ,    pd.Timedelta("nat"),    pd.Timedelta("3 days") ,    pd.Timedelta("4 days"), pd.Timedelta("7 days") ,    pd.Timedelta("nat"),    pd.Timedelta("12 days"),    pd.Timedelta("nat"),    pd.Timedelta("17 days")],   
                              'event3': [pd.Timedelta("nat"),   pd.Timedelta("nat"),    pd.Timedelta("nat"),    pd.Timedelta("nat"),    pd.Timedelta("6 days"), pd.Timedelta("4 days") ,    pd.Timedelta("9 days") ,    pd.Timedelta("nat"),    pd.Timedelta("3 days") ,    pd.Timedelta("nat")]})

incomplete_df['reason'] = "Reason is " + incomplete_df.idxmin(axis="columns")

Issue Description

The above code will throw:
ValueError: attempt to get argmin of an empty sequence

However, using this code:

import pandas as pd
import numpy as np
incomplete_df = pd.DataFrame({'event1': [1,     2     ,np.NAN,5     ,6,np.NAN,np.NAN,11    ,np.NAN,15],
                              'event2': [np.NAN,1     ,np.NAN,3     ,4,7     ,np.NAN,12    ,np.NAN,17],
                              'event3': [np.NAN,np.NAN,np.NAN,np.NAN,6,4     ,9     ,np.NAN,3     ,np.NAN]})

incomplete_df['reason'] = "Reason is " + incomplete_df.idxmin(axis="columns")

returns a dataframe (incomplete_df) with a fourth column with None when the three columns are np.NAN

Expected Behavior

The documentation states:
Raises ValueError If the row/column is empty.

This is currently wrong when it comes to integers.

Expected behaviour:
some consistency between the two datatypes.

With those two stackoverflow posts in mind (https://stackoverflow.com/questions/21188151/pandas-getting-the-name-of-the-minimum-column/73346957#73346957, and https://stackoverflow.com/questions/73354436/pandas-getting-the-name-of-the-minimum-column-with-timedelta-datatype), it is quite obvious, the expected behaviour should not be Raises ValueError If the row/column is empty but rather sets None in the created row/column when the row/column is empty. Or an optional argument should be added to determine what behaviour is desired by the user.

Installed Versions

INSTALLED VERSIONS

commit : e8093ba
python : 3.10.2.final.0
python-bits : 64
OS : Windows
OS-release : 10
Version : 10.0.22000
machine : AMD64
processor : AMD64 Family 25 Model 80 Stepping 0, AuthenticAMD
byteorder : little
LC_ALL : None
LANG : None
LOCALE : English_United Kingdom.1252

pandas : 1.4.3
numpy : 1.22.0
pytz : 2021.3
dateutil : 2.8.2
setuptools : 58.1.0
pip : 22.2.2
Cython : None
pytest : 7.1.2
hypothesis : None
sphinx : None
blosc : None
feather : None
xlsxwriter : None
lxml.etree : None
html5lib : None
pymysql : None
psycopg2 : None
jinja2 : 3.0.3
IPython : 8.0.0
pandas_datareader: None
bs4 : 4.11.1
bottleneck : None
brotli : None
fastparquet : None
fsspec : 2022.5.0
gcsfs : None
markupsafe : 2.0.1
matplotlib : 3.5.2
numba : 0.55.2
numexpr : None
odfpy : None
openpyxl : 3.0.9
pandas_gbq : None
pyarrow : None
pyreadstat : None
pyxlsb : None
s3fs : None
scipy : 1.7.3
snappy : None
sqlalchemy : 1.4.36
tables : None
tabulate : None
xarray : None
xlrd : 2.0.1
xlwt : None
zstandard : None

[josh-medorion]

This method relies on numpy's core/fromnumeric.py, which contains a warning that if the object has a signature different from that of NumPy it will raise a TypeError. Since Timedelta is Pandas specific, I'm guessing that's the source of the problem.

[jreback]

@JasonMendoza2008 bugs are fixed when the community does pull requests

[JasonMendoza2008]

Update:
The bug is still present in the new pandas version (pandas==1.5.2).

[jreback]

@JasonMendoza2008 see my comment above

you are welcome to contribute a patch

bugs are fixed when someone does - pandas is all volunteer

[josh-medorion]

Update: The bug is still present in the new pandas version (pandas==1.5.2).

@JasonMendoza2008 Please stop adding these comments, they only add noise and waste the time of the maintainers. As @jreback has said twice, bugs are not magically fixed, obviously a bug can be assumed to persist in future versions until a fix is contributed.