import numpy as np
import seaborn as sns
import matplotlib.pyplot as plt

pop = int(1.5*10**6)
# Use numpy to generate a normal distribution of the 
sys_pop = np.random.normal(loc=114, scale=11, size=pop)

fig, ax = plt.subplots()

sns.kdeplot(sys_pop, ax=ax, shade=True)
ax.set_title('Distribution of Adult Male Systolic Blood Pressure')
ax.set_xlabel('Systolic BP')

sample_size = 40
sample = np.random.choice(sys_pop, sample_size)

# We can look at the distribution of the values in the sample.

fig, ax = plt.subplots()
sns.distplot(sample, ax=ax, bins=15)
ax.set_title('Sample Distribution of Systolic BP Measurements')

print(f'Sample mean: {sample.mean()}')
print(f'Sample standard deviation: {sample.std()}')
print(f'Sample median: {np.median(sample)}')

number_of_samples = 1000
sample_size = 50
sample_stats = []

for _ in range(number_of_samples):
    sample = np.random.choice(sys_pop, sample_size)
    # collect the mean of each of the 1000 samples in sample stats
    sample_stats.append(sample.mean())

fig, ax = plt.subplots()
ax.hist(sorted(sample_stats), bins=20)
ax.set_title('Sampling Distribution\n of Systolic BP')
ax.set_xlabel("Systolic Blood Pressure")
ax.set_ylabel('Count');

def standard_error(distribution, largest_sample_size, population_std=None):
    
    '''
    Calculate the standard errors for a range of sample sizes
    to demonstrate how standard error decreases when sample 
    size increases.
    '''
 
    std_errors = {}
    
    for sample_size in range(50,largest_sample_size+1):
        sample = np.random.choice(distribution, size=sample_size, replace=True)
        # Standard error with sample distribution standard deviation 
        # in place of population
        if population_std == None:
            std_err = np.std(sample)/np.sqrt(sample_size)
            std_errors[sample_size] = std_err
        
        else:
            std_err = population_std/np.sqrt(sample_size)
            std_errors[sample_size] = std_err
        
    return std_errors
    

std_errors = standard_error(sys_pop, 1000)

fig, ax = plt.subplots()

sns.scatterplot(list(std_errors.keys()), list(std_errors.values()))

std_errors = standard_error(sys_pop, 1000, population_std=114)

fig, ax = plt.subplots()

sns.scatterplot(list(std_errors.keys()), list(std_errors.values()))

var_1 = 'population'
var_2 = 'sample'
var_3 = 'point estimate'
var_4 = 'statistic'
var_5 = 'parameter'
var_6 = 'sampling'


print(f"""We sampled 40 bee hives and calcuted the mean colony population 
          to be 75,690 bees. 75,690 is a {var_1} of the population paramter\n""")

print(f"""We repeatedly sample 40 people at random from Seattle and 
        measure their heart rate,then calculate the mean of each sample. 
        We call the plot of this collection of statistics
        the {var_2} distribution.
        """)

print(f"""There are exactly 58 Javan Rhino's left in the wild. 
        Their mean length has been measured accurately at 5 feet.
        This mean length is considered a population {var_3}. 
        """)

print(f"""If we plot a histogram of individual pistil lengths 
      measured on 50 hibiscus flowers, we would be plotting the distribution 
      of an attribute of our {var_4} of hibiscus flowers. 
        """)

print(f"""Since every restaurant in Chicago is required by law to register
        with the city, we can accurately count the number of active pizza restaurants
         operating right now.  This group represents the {var_5} of actively 
        operating, registered pizza restaurants in Chicago.
    """)

print(f"""The mean number of hourly hits to Jelle's Marble Racing website 
            randomly sampled across a seven day period represents a sample
            {var_6}.
        """)

#__SOLUTION__
# Word Exercise

var_1 = 'population'
var_2 = 'sample'
var_3 = 'point estimate'
var_4 = 'statistic'
var_5 = 'parameter'
var_6 = 'sampling'


print(f"""We sampled 40 bee hives and calcuted the mean colony population 
          to be 75,690 bees. 75,690 is a {var_3} of the population paramter\n""")

print(f"""We repeatedly sample 40 people at random from Seattle and 
        measure their heart rate,then calculate the mean of each sample. 
        We call the plot of this collection of statistics
        the {var_6} distribution.
        """)

print(f"""There are exactly 58 Javan Rhino's left in the wild. 
        Their mean length has been measured accurately at 5 feet.
        This mean length is considered a population {var_5}. 
        """)

print(f"""If we plot a histogram of individual pistil lengths 
      measured on 50 hibiscus flowers, we would be plotting the distribution 
      of an attribute of our {var_2} of hibiscus flowers. 
        """)

print(f"""Since every restaurant in Chicago is required by law to register
        with the city, we can accurately count the number of active pizza restaurants
        actively operating right now.  This group represents the {var_1} of actively 
        operating, registered pizza restaurants in Chicago.
    """)

print(f"""The mean number of hourly hits to Jelle's Marble Racing website 
            randomly sampled across a seven day period represents a sample
            {var_4}.
        """)

mccalister = ['Adam', 'Amanda','Chum', 'Dann', 
 'Jacob', 'Jason', 'Johnhoy', 'Karim', 
'Leana','Luluva', 'Matt', 'Maximilian' ]

for n in range(1,4):
    group = np.random.choice(mccalister, 4, replace=False)
    print(f'group {n}', group)
    for name in list(group):
        mccalister.remove(name)

population = np.random.binomial(12, .6, 10000)
fig, ax = plt.subplots()
ax.bar(range(0,12), np.unique(population, return_counts=True)[1])
ax.set_title('Strikes Per Game')

#__SOLUTION__

sample_means = []
for n in range(1000):
    sample = np.random.choice(population, 50)
    sample_means.append(sample.mean())
    
fig, ax = plt.subplots()
ax.hist(sample_means, bins = 20)

mail_population = np.random.poisson(3, 4500)
counts = np.unique(mail_population, return_counts=True)

fig, ax = plt.subplots()
ax.bar(np.unique(counts[0]), counts[1])
ax.set_title('Distribution of Pieces of Mail/Week')
ax.set_xlabel("Pieces of Mail")

#__SOLUTION__

sample_means = []
for n in range(1000):
    sample = np.random.choice(mail_population, 50)
    sample_means.append(sample.mean())
    
fig, ax = plt.subplots()
ax.hist(sample_means, bins = 30)
ax.set_title('Sample Means of Pieces of Mail\n Arriving at your door')
ax.set_xlabel('Number of pieces of mail')

# on average, 20 customers enter per hour
piggly_population = np.random.exponential(1/(20/60), size=10000)
fig, ax = plt.subplots()
ax.hist(piggly_population, bins = 50, normed=True)
ax.set_title('Sample Means of Time Between Piggle Wiggly Customers')
ax.set_xlabel('Minutes');

#__SOLUTION__

sample_means = []
for n in range(1000):
    sample = np.random.choice(piggly_population, 50)
    sample_means.append(sample.mean())
    
fig, ax = plt.subplots()
ax.hist(sample_means, bins = 30);
ax.set_title("""Sample means of number of minutes\n between people entering a Piggly Wiggly""")
ax.set_xlabel("Number of minutes between customers")

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import requests
%matplotlib inline

! wget 'https://s3.amazonaws.com/capitalbikeshare-data/201905-capitalbikeshare-tripdata.zip' -O temp.zip
! unzip temp.zip

df = pd.read_csv('201905-capitalbikeshare-tripdata.csv')

df.tail()

import seaborn as sns
from scipy import stats

fig, ax = plt.subplots(2,1, figsize=(10,10))
sns.distplot(df.Duration, bins = 20, ax=ax[0])
sns.boxplot(df.Duration, ax=ax[1])

pop_no_fliers = df[np.abs(stats.zscore(df.Duration) > 3)]

fig, ax = plt.subplots()
sns.distplot(pop_no_fliers.Duration)

member_df = df[df['Member type'] == 'Member']
casual_df = df[df['Member type'] == 'Casual']

plt.boxplot(member_df['Duration']);

from scipy import stats
print(member_df.shape)
sum(stats.zscore(member_df.Duration)>3)

member_df_nofliers = member_df[np.abs(stats.zscore(member_df.Duration)) < 3]
member_df_nofliers.shape

import seaborn as sns
fig, ax = plt.subplots()
sns.distplot(member_df_nofliers.Duration, bins = 20, ax=ax);

fig, ax = plt.subplots()
sns.boxplot(casual_df.Duration)

casual_df_nofliers = casual_df[np.abs(stats.zscore(casual_df.Duration)) < 3]

fig, ax = plt.subplots()
sns.distplot(casual_df_nofliers.Duration, bins=20, ax=ax)

fig, ax = plt.subplots()
sns.distplot(member_df_nofliers.Duration, bins = 20, ax=ax, color='blue');
sns.distplot(casual_df_nofliers.Duration, bins=20, ax=ax, color='green')

df.median()

pop_mean = df.Duration.mean()
pop_std = df.Duration.std()
print(f'pop_mean is {pop_mean} \npop_std is {pop_std}')

def one_sample_mean(population):
    sample = np.random.choice(population, size=200, replace=True)
    return sample.mean()

one_sample_mean(df.Duration)

d = [one_sample_mean(df.Duration) for i in range(1000)]
plt.hist(d, bins=50)

import seaborn as sns

def central_limit_theorem_plotter(distribution, sample_size, num_samples, color='blue'):
    sample_means = np.zeros(num_samples)
    for idx, num in enumerate(range(num_samples)):
        sample = np.random.choice(distribution, size=sample_size, replace=True)
        sample_means[idx] = sample.mean()
    sns.distplot(sample_means, bins=80, kde=True,  color=color)
    title = f'Sample Distribution n = {sample_size} and number of samples = {num_samples},\
    std error = {pop_std / num_samples}'
    print(f'mean = {sample_means.mean()}')
    plt.title(title)

central_limit_theorem_plotter(df.Duration, 1000, 500);

central_limit_theorem_plotter(df.Duration, 5000, 50);

central_limit_theorem_plotter(member_df.Duration, 1000, 500, 'blue')
central_limit_theorem_plotter(casual_df.Duration, 1000, 500, 'green')