Distribution of generated numbers by a given total sum

dist.py

from matplotlib import pyplot as plt

def validate(func, s=100, n=5, trails=100000):
    counts = [0] * (s + 1)
    for _ in xrange(trails):
        for x in func(s, n):
            counts[x] += 1
    plt.plot(range(s + 1), counts)
    plt.show()

import random

def rescale_gen(s, n):
    while True:
        xs = [random.random() for _ in xrange(n)]
        s1 = sum(xs)
        xs = [int(x * s / s1 + .5) for x in xs]
        xs[0] = s - sum(xs[1:])
        if xs[0] >= 0:
            break
    return xs

def sort_gen(s, n):
    seps = [random.randint(0, s) for _ in xrange(n - 1)]
    seps.sort()
    seps.append(s)
    seps.append(0)
    xs = [seps[i] - seps[i - 1] for i in xrange(n)]
    return xs

# validate(rescale_gen)
validate(sort_gen)