Basic Examples (2) 

Ask five hundred people when their birthday is and count the number of distinct results:

In[1]:=

Out[1]=

Based on that result, make an estimate for the number of days in a year:

In[2]:=

Out[2]=

Calculate the number of birthdays for Saturn, but keep the number secret:

In[3]:=

Count the number of distinct results in fifty thousand random birthdays on Saturn:

In[4]:=

Out[4]=

With sample sizes 50,000 and 21,265, distinct results estimate how many days per year there are on Saturn:

In[5]:=

Out[5]=

Applications (2) 

Sample sorted subsets and use that to estimate the the full support size:

In[6]:=

Out[6]=

The actual answer:

In[7]:=

Out[7]=

Possible Issues (2) 

Sample sorted 4-tuples and use that to estimate the the full support size:

In[8]:=

Out[8]=

This sampling method is not uniformly distributed, so the support size estimate is an undercount:

In[9]:=

Out[9]=

If the number of distinct items is the same as the sample size, you will need a larger sample.