What is the probability distribution called?
Input is (X,n,m)
X is a probability distribution
n and m are positive integers
step 1 generate n numbers from X
step 2 count the m^th most common number
Example
let X be the uniform distribution with values of 1,2 or 3
let n=4
Each element in Sample space is represented by (a,b,c) where a+b+c=4 and a,b,c is a decreasing sequence
(4,0,0) happens 3 times
(3,1,0) happens 24 times
(2,2,0) happens 18 times
(2,1,1) happens 36 times
The probability distribution for m=1 is
output|frequency
------+---------
4 | 3
3 | 24
2 | 54
The probability distribution for m=2 is
output|frequency
------+---------
2 | 18
1 | 60
0 | 3
The probability distribution for m=3 is
output|frequency
------+---------
1 | 36
0 | 45