# 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(
) #not optimal to plot histogram when results are integers, hard to read
plt.close()
#will the bank fail?
#ecdf is read: trials with 10 defaults OR LESS if ~100%
# Compute ECDF: x, y
from ecdf_func import ecdf
x, y = ecdf(n_defaults)
# Plot the ECDF with labeled axes
_ = plt.plot(x, y, marker='.', linestyle='none')
_ = plt.xlabel('number of defaults')
_ = plt.ylabel('percentage defaults')
# 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)
print(n_lose_money)
# Compute and print probability of losing money
print('Probability of losing money =', n_lose_money / len(n_defaults))
#interest rate is such that banks will lose money if 10 or more
# -*- coding: utf-8 -*-
"""
Created on Sun Nov 19 14:36:18 2017
@author: James
"""
import numpy as np
from ecdf_func import ecdf
from pmf_func import pmf_plot
import matplotlib.pyplot as plt
samples = np.random.poisson(6, size=10000)
x, y = ecdf(samples)
pmf_plot(samples)
_ = plt.plot(x, y, marker='.', linestyle='none')
plt.margins(0.02)
_ = plt.xlabel('number of sucesses')
_ = plt.ylabel('CDF')
plt.show()
plt.close()
#relationship between Binomial and Poisson distributions
# Print the result with some nice formatting
print('I. versicolor:', mean_length_vers, 'cm')
#computing percentiles
# Specify array of percentiles: percentiles
percentiles = np.array([2.5, 25, 50, 75, 97.5])
# Compute percentiles: ptiles_vers
ptiles_vers = np.percentile(versicolor_petal_length, percentiles)
# Print the result
print(ptiles_vers)
#comparing percentiles to ECDF
from ecdf_func import ecdf
x_vers, y_vers = ecdf(versicolor_petal_length)
# Plot the ECDF
_ = plt.plot(x_vers, y_vers, '.')
plt.margins(0.02)
_ = plt.xlabel('petal length (cm)')
_ = plt.ylabel('ECDF')
# Overlay percentiles as red diamonds.
_ = plt.plot(ptiles_vers,
percentiles / 100,
marker='D',
color='red',
linestyle='none')
# Show the plot
plt.show()
from ecdf_func import ecdf
import matplotlib.pyplot as plt
import seaborn as sns
sns.set()
michelson_speed_of_light = pd.read_csv(
'michelson_speed_of_light.csv')['velocity of light in air (km/s)']
mean = np.mean(michelson_speed_of_light)
std = np.std(michelson_speed_of_light)
samples = np.random.normal(mean, std, size=10000)
x, y = ecdf(michelson_speed_of_light)
x_theor, y_theor = ecdf(samples)
_ = plt.plot(x_theor, y_theor)
_ = plt.plot(x, y, marker='.', linestyle='none')
_ = plt.xlabel('speed of light (km/s)')
_ = plt.ylabel('CDF')
plt.show()
plt.close()
import matplotlib.pyplot as plt
np.random.binomial(4, 0.5, size=10) #repeat the 4 flip experiement 10 times
samples = np.random.binomial(60, 0.1, size=10000)
_ = plt.hist(samples)
plt.show()
plt.close()
from ecdf_func import ecdf
import seaborn as sns
sns.set()
x, y = ecdf(samples)
_ = plt.plot(x, y, marker='.', linestyle='none')
plt.margins(0.2)
_ = plt.xlabel('number of successes')
_ = plt.ylabel('CDF')
plt.show()
plt.close()
#sampling out of the binoimal distribution
# Take 10,000 samples out of the binomial distribution: n_defaults
import numpy as np
import matplotlib.pyplot as plt
from Bernoulli_Trial import perform_bernoulli_trials
from ecdf_func import ecdf
# Seed random number generator
np.random.seed(42)
# Take 10,000 samples out of the binomial distribution: n_defaults
n_defaults = np.random.binomial(100, 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.margins(0.002)
plt.xlabel('Defaults out of 100 loans')
plt.ylabel('ECDF')
# Show the plot
plt.show()
# ################################################################## #
# Seed random number generator
np.random.seed(42)
df = pd.DataFrame(data['data'], columns=data['feature_names'])
df['target'] = data['target']
#replace the 0,1,2 with species names
for idx, species in enumerate(data['target_names']):
print(idx, species)
df['target'].replace(idx, species, inplace=True)
df.rename(columns={'target': 'species'}, inplace=True)
versicolor_petal_length = df[df['species'] ==
'versicolor']['petal length (cm)']
setosa_petal_length = df[df['species'] == 'setosa']['petal length (cm)']
virginica_petal_length = df[df['species'] == 'virginica']['petal length (cm)']
# Compute ECDF for versicolor data: x_vers, y_vers
x_vers, y_vers = ecdf(versicolor_petal_length)
# Generate plot
_ = plt.plot(x_vers, y_vers, marker='.', linestyle='none')
# Make the margins nice
_ = plt.margins(0.02)
# Label the axes
_ = plt.xlabel("versicolor_petal_length")
_ = plt.ylabel("ECDF")
# Display the plot
plt.show()
plt.close()
import numpy as np
import matplotlib.pyplot as plt
# import pandas as pd
from ecdf_func import ecdf
# Compute mean and standard deviation: mu, sigma
mu = np.mean(belmont_no_outliers)
sigma = np.std(belmont_no_outliers)
# Sample out of a normal distribution with this mu and sigma: samples
samples = np.random.normal(mu, sigma, size=10000)
# Get the CDF of the samples and of the data
x_theor, y_theor = ecdf(samples)
x, y = ecdf(belmont_no_outliers)
# Plot the CDFs and show the plot
_ = plt.plot(x_theor, y_theor)
_ = plt.plot(x, y, marker='.', linestyle='none')
plt.margins(0.02)
_ = plt.xlabel('Belmont winning time (sec.)')
_ = plt.ylabel('CDF')
plt.show()
# Take a million samples out of the Normal distribution: samples
samples = np.random.normal(mu, sigma, size=1000000)
# Compute the fraction that are faster than 144 seconds: prob
prob = np.sum(samples <= 144) / len(samples)
# -*- coding: utf-8 -*- """ Created on Mon Nov 20 00:40:06 2017 @author: James """ import numpy as np from ecdf_func import ecdf #exponential inter-incident times inter_times = 500 mean = np.mean(inter_times) samples = np.random.exponential(mean, size=10000) x, y = ecdf(inter_times)
