How to get N random integer numbers whose sum is equal to M

Question

I want to make a list of N random INTEGER numbers whose sum is equal to M number.

I have used numpy and dirichlet function in Python, but this generate double random number array, I would like to generate integer random number.

import numpy as np 
np.random.dirichlet(np.ones(n))*m

The solution can use other distribution the sense is resolve the problem.

Answer 1

The problem with using dirichlet for this is that it is a distribution over real numbers. It will yield a vector of numbers in the range (0,1), which sum to 1, but truncating or rounding them may remove the guarantee of a specific sum. Following this post we can get the desired effect from the multinomial distribution (using np.random.multinomial), as follows:

from numpy.random import multinomial

np.random.multinomial(m, np.ones(n)/n)

This will generate n integers between 0 and m, whose sum is m, with equal probability of drawing a given position. The easiest way to visualize this is to consider the result as describing a set of draws from a fixed set of objects (e.g., die rolls drawing from the integers from 1 to 6) where the final array is the number of times the corresponding object was drawn. The total will always sum to the given number of total draws (rolls).