from collections import defaultdict

import numpy as np

n = 10
z = np.random.random(n)
z = z / np.sum(z)

total_cnt = 100000
cnts = defaultdict(int)
for i in range(total_cnt):
    u = np.random.uniform(size=n)
    g = -np.log(-np.log(u))
    x = np.argmax(g + np.log(z))
    cnts[x] += 1

print(np.var(np.array([cnts[x] for x in cnts.keys()]) / float(total_cnt) - z))