bernoulli_distribution.py

from __future__ import division
import random
import math
import matplotlib.pyplot as plt
from normal_distribution import normal_pdf
from normal_distribution import normal_cdf
from collections import Counter


def bernoulli_trial(p):
    return 1 if random.random() < p else 0

def binomial(n, p):
    return sum(bernoulli_trial(p) for i in range(n))

def make_hist(p, n, num_points):
    data = [binomial(n ,p) for _ in range(num_points)]

    #use a bar chart to show the actual binomial samples
    histogram = Counter(data)
    plt.bar([x - 0.4 for x in histogram.keys()],
            [v / num_points for v in histogram.values()],
            0.8,
            color='0.75')

    mu = p * n
    sigma = math.sqrt(n * p * (1-p))

    #use a line chart to show the normal approx.
    xs = range(min(data), max(data) + 1)
    ys = [normal_cdf(1 + 0.5, mu, sigma) - normal_cdf(i - 0.5, mu, sigma)
          for i in xs]
    plt.plot(xs,ys)
    plt.title("Binomal Distribution vs. Normal Approximation")
    plt.show()

def main():
    make_hist(0.75, 100, 10000)


if __name__ == "__main__": main()