central_limit_theorem.py

import numpy as np
import matplotlib
from math import sqrt
matplotlib.use('TkAgg')
import matplotlib.pyplot as plt


def binomial_to_normal(samples, trials, probability, bins=50):
    data = []
    for i in range(samples):
        vals = np.random.binomial(trials, probability, samples)
        data.append(np.sum(vals) / sqrt(samples) / np.std(vals))
    plt.hist(data, bins, normed=True)
    plt.show()


def poisson_to_normal(samples, lambda_num, bins=50):
    data = []
    for i in range(samples):
        vals = np.random.poisson(lambda_num, samples)
        data.append(np.sum(vals) / sqrt(samples) / np.std(vals))
    plt.hist(data, bins, normed=True)
    plt.show()


def main():
    samples = 5000
    trials = 200
    prob = 0.4
    poisson_to_normal(samples, 50, 40)
    binomial_to_normal(samples, trials, prob, 50)


if __name__ == '__main__':
    main()