Examples
By default, the product of an empty or all-NA Series is 1.

In [1]:
import numpy as np
import pandas as pd
In [2]:
pd.Series([]).prod()
Out[2]:
1.0

This can be controlled with the min_count parameter

In [5]:
pd.Series([]).prod(min_count=1)
Out[5]:
nan

Thanks to the skipna parameter, min_count handles all-NA and empty series identically.

In [6]:
pd.Series([np.nan]).prod()
Out[6]:
1.0
In [7]:
pd.Series([np.nan]).prod(min_count=1)
Out[7]:
nan