python-numpy-伯努利试验模拟-np.random.binomial--自定义bins的直方图

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

贷款违约率的模拟# 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()ecdf曲线：# Compute ECDF: x, y
x,y=ecdf(n_defaults)

# Plot the ECDF with labeled axes
plt.plot(x,y,marker='.',linestyle='none')
plt.xlabel('x')
plt.ylabel('y')

# Show the plot
plt.show()

# Compute the number of 100-loan simulations with 10 or more defaults: n_lose_money
n_lose_money=np.sum(n_defaults>=10)

# Compute and print probability of losing money
print('Probability of losing money =', n_lose_money / len(n_defaults))另一种简便的方法：# Take 10,000 samples out of the binomial distribution: n_defaults
n_defaults=np.random.binomial(n=100,p=0.05,size=10000)

# Compute CDF: x, y
x,y=ecdf(n_defaults)

# Plot the CDF with axis labels
plt.plot(x,y,marker = '.',linestyle = 'none')
plt.xlabel('he number of defaults out of 100 loans,')
plt.ylabel('CDF')

# Show the plot
plt.show()画直方图，自定义bins# Compute bin edges: bins
bins = np.arange(0, max(n_defaults) + 1.5) - 0.5

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

# Set margins
plt.margins(0.02)

# Label axes
plt.xlabel('违约')
plt.ylabel('数目')

# Show the plot
plt.show()