Hack_Bern_nprandom.py

# -*- coding: utf-8 -*-
"""
Created on Tue Mar  7 21:39:58 2017

@author: Shabaka
"""
import numpy as np
import matplotlib.pyplot as plt


def perform_bernoulli_trials(n, p):
    """Perform n Bernoulli trials with success probability p
    and return number of successes."""
    # Initialize number of successes: n_success
    n_success = 0

    # Perform trials
    for i in range(n):
        # Choose random number between zero and one: random_number
        random_number = np.random.random()

        # If less than p, it's a success so add one to n_success
        if random_number < p:
            n_success += 1

    return n_success

# Seed random number generator
np.random.seed(42)

# Initialize the number of defaults: n_defaults
n_defaults = np.empty(1000)

# Compute the number of defaults
for i in range(1000):
    n_defaults[i] = perform_bernoulli_trials(100, 0.05)


# Plot the histogram with default number of bins; label your axes
_ = plt.hist(n_defaults, normed=True)
_ = plt.xlabel('number of defaults out of 100 loans')
_ = plt.ylabel('probability')

# Show the plot
plt.show()

# Compute bin edges: bins
bins = np.arange(-0.5, max(n_defaults + 1.5) - 0.5)

# Generate histogram
_ = plt.hist(n_defaults, normed=True, bins=bins)

# Set margins
plt.margins(0.02)

# Label axes
_ = plt.xlabel('number of defaults out of 100 loans')
_ = plt.ylabel('Binomial PMF')


# Show the plot
plt.show()


# Draw 10,000 samples out of Poisson distribution: samples_poisson
samples_poisson = np.random.poisson(10, size=10000)

# Print the mean and standard deviation
print('Poisson:     ', np.mean(samples_poisson),
                       np.std(samples_poisson))

# Specify values of n and p to consider for Binomial: n, p
n = [20, 100, 1000]
p = [0.5, 0.1, 0.01]


# Draw 10,000 samples for each n,p pair: samples_binomial
for i in range(3):
    samples_binomial = np.random.binomial(n[i], p[i], size=10000)

    # Print results
    print('n =', n[i], 'Binom:', np.mean(samples_binomial),
                                 np.std(samples_binomial))