Pandas aggregate count distinct
'nunique' is an option for .agg() since pandas 0.20.0, so:
df.groupby('date').agg({'duration': 'sum', 'user_id': 'nunique'})
How about either of:
>>> df
date duration user_id
0 2013-04-01 30 0001
1 2013-04-01 15 0001
2 2013-04-01 20 0002
3 2013-04-02 15 0002
4 2013-04-02 30 0002
>>> df.groupby("date").agg({"duration": np.sum, "user_id": pd.Series.nunique})
duration user_id
date
2013-04-01 65 2
2013-04-02 45 1
>>> df.groupby("date").agg({"duration": np.sum, "user_id": lambda x: x.nunique()})
duration user_id
date
2013-04-01 65 2
2013-04-02 45 1