poisson_appx.py

poisson_appx.py

import numpy as np
from scipy import stats
import matplotlib.pyplot as plt


def compare(n, p):
    return np.sum([abs(stats.poisson.pmf(x, n*p) - stats.binom.pmf(x, n, p)) for x in range(100)])


max_moneysupply = 1e16

min_balance = 1e6
max_balance = 1e15

max_committee = 60
min_committee = 30

iters = 1e5

money = np.random.randint(int(min_balance), int(max_moneysupply), int(iters))
committee = np.random.randint(int(min_committee), int(max_committee), int(iters))
moneysupply = np.random.randint(int(max_balance), int(max_moneysupply), int(iters))


deltas = np.zeros(int(iters))
for x in range(len(deltas)):
  if x % 100 == 0: 
    print(x)
  deltas[x] = compare(money[x], float(committee[x])/float(moneysupply[x]))


plt.hist(deltas, bins=25)
plt.savefig("poisson_appx.png")