So here is the deal: I want to (for example) generate 4 pseudo-random numbers, that when added together would equal 40. How could this be dome in python? I could generate a random number 1-40, then generate another number between 1 and the remainder,etc, but then the first number would have a greater chance of "grabbing" more.
7 Answers
If you want true randomness then use:
import numpy as np
def randofsum_unbalanced(s, n):
# Where s = sum (e.g. 40 in your case) and n is the output array length (e.g. 4 in your case)
r = np.random.rand(n)
a = np.array(np.round((r/np.sum(r))*s,0),dtype=int)
while np.sum(a) > s:
a[np.random.choice(n)] -= 1
while np.sum(a) < s:
a[np.random.choice(n)] += 1
return a
If you want a greater level of uniformity then take advantage of the multinomial distribution:
def randofsum_balanced(s, n):
return np.random.multinomial(s,np.ones(n)/n,size=1)[0]
Building on @markdickonson by providing some control over distribution between the divisors. I introduce a variance/jiggle as a percentage of the uniform distance between each.
def constrained_sum_sample(n, total, variance=50):
"""Return a random-ish list of n positive integers summing to total.
variance: int; percentage of the gap between the uniform spacing to vary the result.
"""
divisor = total/n
jiggle = divisor * variance / 100 / 2
dividers = [int((x+1)*divisor + random.random()*jiggle) for x in range(n-1)]
result = [a - b for a, b in zip(dividers + [total], [0] + dividers)]
return result
Sample output:
[12, 8, 10, 10]
[10, 11, 10, 9]
[11, 9, 11, 9]
[11, 9, 12, 8]
The idea remains to divide the population equally, then randomly move them left or right within the given range. Since each value is still bound to the uniform point we don't have to worry about it drifting.
Good enough for my purposes, but not perfect. eg: the first number will always vary higher, and the last will always vary lower.
Related