Index and Series min and max handles nan and NaT differently. Even though min and max are defined in IndexOpsMixin, Series doesn't use them and use NDFrame definitions.
pd.Index([np.nan, 1.0]).min()
# nan
pd.Index([np.nan, 1.0]).max()
# nan
pd.DatetimeIndex([pd.NaT, '2011-01-01']).min()
# NaT
pd.DatetimeIndex([pd.NaT, '2011-01-01']).max()
#2011-01-01 00:00:00
# Series excludes nan and NaT
pd.Series([np.nan, 1.0]).min()
#1.0
pd.Series([np.nan, 1.0]).max()
#1.0
pd.Series([pd.NaT, pd.Timestamp('2011-01-01')]).min()
#2011-01-01 00:00:00
pd.Series([pd.NaT, pd.Timestamp('2011-01-01')]).max()
#2011-01-01 00:00:00
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