Econometrics-With-Python/plot_material.py at main · weijie-chen/Econometrics-With-Python · GitHub

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import datetime as dt

import matplotlib.pyplot as plt

import numpy as np

import pandas as pd

import pandas_datareader as pdr

import scipy as sp

import scipy.stats

import statsmodels.api as sm

###############################################################################################################

def reg_corr_plot():

class LinearRegression:

def __init__(self, beta1, beta2, error_scale, data_size):

self.beta1 = beta1

self.beta2 = beta2

self.error_scale = error_scale

self.x = np.random.randint(1, data_size, data_size)

self.y = (

self.beta1

+ self.beta2 * self.x

+ self.error_scale * np.random.randn(data_size)

)

def x_y_cor(self):

return np.corrcoef(self.x, self.y)[0, 1]

fig, ax = plt.subplots(nrows=2, ncols=4, figsize=(24, 12))

beta1, beta2, error_scale, data_size = 2, 0.05, 1, 100

lrg1 = LinearRegression(beta1, beta2, error_scale, data_size)

ax[0, 0].scatter(lrg1.x, lrg1.y)

ax[0, 0].plot(lrg1.x, beta1 + beta2 * lrg1.x, color="#FA954D", alpha=0.7)

ax[0, 0].set_title(r"$Y={}+{}X+{}u$".format(beta1, beta2, error_scale))

ax[0, 0].annotate(

r"$\rho={:.4}$".format(lrg1.x_y_cor()), xy=(0.1, 0.9), xycoords="axes fraction"

)

beta1, beta2, error_scale, data_size = 2, -0.6, 1, 100

lrg2 = LinearRegression(beta1, beta2, error_scale, data_size)

ax[0, 1].scatter(lrg2.x, lrg2.y)

ax[0, 1].plot(lrg2.x, 2 - 0.6 * lrg2.x, color="#FA954D", alpha=0.7)

ax[0, 1].set_title(r"$Y={}+{}X+{}u$".format(beta1, beta2, error_scale))

ax[0, 1].annotate(

r"$\rho={:.4}$".format(lrg2.x_y_cor()), xy=(0.1, 0.9), xycoords="axes fraction"

)

beta1, beta2, error_scale, data_size = 2, 1, 1, 100

lrg3 = LinearRegression(beta1, beta2, error_scale, data_size)

ax[0, 2].scatter(lrg3.x, lrg3.y)

ax[0, 2].plot(lrg3.x, beta1 + beta2 * lrg3.x, color="#FA954D", alpha=0.7)

ax[0, 2].set_title(r"$Y={}+{}X+{}u$".format(beta1, beta2, error_scale))

ax[0, 2].annotate(

r"$\rho={:.4}$".format(lrg3.x_y_cor()), xy=(0.1, 0.9), xycoords="axes fraction"

)

beta1, beta2, error_scale, data_size = 2, 3, 1, 100

lrg4 = LinearRegression(beta1, beta2, error_scale, data_size)

ax[0, 3].scatter(lrg4.x, lrg4.y)

ax[0, 3].plot(lrg4.x, beta1 + beta2 * lrg4.x, color="#FA954D", alpha=0.7)

ax[0, 3].set_title(r"$Y={}+{}X+{}u$".format(beta1, beta2, error_scale))

ax[0, 3].annotate(

r"$\rho={:.4}$".format(lrg4.x_y_cor()), xy=(0.1, 0.9), xycoords="axes fraction"

)

beta1, beta2, error_scale, data_size = 2, 3, 3, 100

lrg5 = LinearRegression(beta1, beta2, error_scale, data_size)

ax[1, 0].scatter(lrg5.x, lrg5.y)

ax[1, 0].plot(lrg5.x, beta1 + beta2 * lrg5.x, color="#FA954D", alpha=0.7)

ax[1, 0].set_title(r"$Y={}+{}X+{}u$".format(beta1, beta2, error_scale))

ax[1, 0].annotate(

r"$\rho={:.4}$".format(lrg5.x_y_cor()), xy=(0.1, 0.9), xycoords="axes fraction"

)

beta1, beta2, error_scale, data_size = 2, 3, 10, 100

lrg6 = LinearRegression(beta1, beta2, error_scale, data_size)

ax[1, 1].scatter(lrg6.x, lrg6.y)

ax[1, 1].plot(lrg6.x, beta1 + beta2 * lrg6.x, color="#FA954D", alpha=0.7)

ax[1, 1].set_title(r"$Y={}+{}X+{}u$".format(beta1, beta2, error_scale))

ax[1, 1].annotate(

r"$\rho={:.4}$".format(lrg6.x_y_cor()), xy=(0.1, 0.9), xycoords="axes fraction"

)

beta1, beta2, error_scale, data_size = 2, 3, 20, 100

lrg7 = LinearRegression(beta1, beta2, error_scale, data_size)

ax[1, 2].scatter(lrg7.x, lrg7.y)

ax[1, 2].plot(lrg7.x, beta1 + beta2 * lrg7.x, color="#FA954D", alpha=0.7)

ax[1, 2].set_title(r"$Y={}+{}X+{}u$".format(beta1, beta2, error_scale))

ax[1, 2].annotate(

r"$\rho={:.4}$".format(lrg7.x_y_cor()), xy=(0.1, 0.9), xycoords="axes fraction"

)

beta1, beta2, error_scale, data_size = 2, 3, 50, 100

lrg8 = LinearRegression(beta1, beta2, error_scale, data_size)

ax[1, 3].scatter(lrg8.x, lrg8.y)

ax[1, 3].plot(lrg3.x, beta1 + beta2 * lrg3.x, color="#FA954D", alpha=0.7)

ax[1, 3].set_title(r"$Y={}+{}X+{}u$".format(beta1, beta2, error_scale))

ax[1, 3].annotate(

r"$\rho={:.4}$".format(lrg8.x_y_cor()), xy=(0.1, 0.9), xycoords="axes fraction"

)

###############################################################################################################

def central_limit_theorem_plot():

fig, ax = plt.subplots(4, 3, figsize=(20, 20))

########################################################################################

x = np.linspace(2, 8, 100)

a = 2 # range of uniform distribution

b = 8

unif_pdf = np.ones(len(x)) * 1 / (b - a)

ax[0, 0].plot(x, unif_pdf, lw=3, color="r")

ax[0, 0].plot(

[x[0], x[0]], [0, 1 / (b - a)], lw=3, color="r", alpha=0.9

) # vertical line

ax[0, 0].plot([x[-1], x[-1]], [0, 1 / (b - a)], lw=3, color="r", alpha=0.9)

ax[0, 0].fill_between(x, 1 / (b - a), 0, alpha=0.5, color="r")

ax[0, 0].set_xlim([1, 9])

ax[0, 0].set_ylim([0, 0.4])

ax[0, 0].set_title("Uniform Distribution", size=18)

ax[0, 0].set_ylabel("Population Distribution", size=12)

########################################################################################

ss = 2 # sample size

unif_sample_mean = np.zeros(1000)

for i in range(1000):

unif_sample = np.random.rand(ss)

unif_sample_mean[i] = np.mean(unif_sample)

ax[1, 0].hist(unif_sample_mean, bins=20, color="r", alpha=0.5)

ax[1, 0].set_ylabel("Sample Distribution， $n = 2$", size=12)

########################################################################################

ss = 10 # sample size

unif_sample_mean = np.zeros(1000)

for i in range(1000):

unif_sample = np.random.rand(ss)

unif_sample_mean[i] = np.mean(unif_sample)

ax[2, 0].hist(unif_sample_mean, bins=30, color="r", alpha=0.5)

ax[2, 0].set_ylabel("Sample Distribution, $n = 10$", size=12)

########################################################################################

ss = 1000 # sample size

unif_sample_mean = np.zeros(1000)

for i in range(1000):

unif_sample = np.random.rand(ss)

unif_sample_mean[i] = np.mean(unif_sample)

ax[3, 0].hist(unif_sample_mean, bins=40, color="r", alpha=0.5)

ax[3, 0].set_ylabel("Sample Distribution, $n = 1000$", size=12)

########################################################################################

a = 6

b = 2

x = np.linspace(0, 1, 100)

beta_pdf = sp.stats.beta.pdf(x, a, b)

ax[0, 1].plot(x, beta_pdf, lw=3, color="g")

ax[0, 1].set_ylim([0, 6])

ax[0, 1].fill_between(x, beta_pdf, 0, alpha=0.5, color="g")

ax[0, 1].set_title("Beta Distribution", size=18)

########################################################################################

ss = 2 # sample size

beta_sample_mean = np.zeros(1000)

for i in range(1000):

beta_sample = sp.stats.beta.rvs(a, b, size=ss)

beta_sample_mean[i] = np.mean(beta_sample)

ax[1, 1].hist(beta_sample_mean, color="g", alpha=0.5)

########################################################################################

ss = 10 # sample size

beta_sample_mean = np.zeros(1000)

for i in range(1000):

beta_sample = sp.stats.beta.rvs(a, b, size=ss)

beta_sample_mean[i] = np.mean(beta_sample)

ax[2, 1].hist(beta_sample_mean, color="g", bins=20, alpha=0.5)

########################################################################################

ss = 100000 # sample size

beta_sample_mean = np.zeros(1000)

for i in range(1000):

beta_sample = sp.stats.beta.rvs(a, b, size=ss)

beta_sample_mean[i] = np.mean(beta_sample)

ax[3, 1].hist(beta_sample_mean, color="g", bins=30, alpha=0.5)

########################################################################################

a = 6

x = np.linspace(0, 25, 100)

gamma_pdf = sp.stats.gamma.pdf(x, a)

ax[0, 2].plot(x, gamma_pdf, lw=3, color="b")

ax[0, 2].set_ylim([0, 0.34])

ax[0, 2].fill_between(x, gamma_pdf, 0, alpha=0.5, color="b")

ax[0, 2].set_title("Gamma Distribution", size=18)

########################################################################################

ss = 2 # sample size

gamma_sample_mean = np.zeros(1000)

for i in range(1000):

gamma_sample = sp.stats.gamma.rvs(a, size=ss)

gamma_sample_mean[i] = np.mean(gamma_sample)

ax[1, 2].hist(gamma_sample_mean, color="b", alpha=0.5)

########################################################################################

ss = 10 # sample size

gamma_sample_mean = np.zeros(1000)

for i in range(1000):

gamma_sample = sp.stats.gamma.rvs(a, size=ss)

gamma_sample_mean[i] = np.mean(gamma_sample)

ax[2, 2].hist(gamma_sample_mean, bins=20, color="b", alpha=0.5)

########################################################################################

ss = 1000 # sample size

gamma_sample_mean = np.zeros(1000)

for i in range(1000):

gamma_sample = sp.stats.gamma.rvs(a, size=ss)

gamma_sample_mean[i] = np.mean(gamma_sample)

ax[3, 2].hist(gamma_sample_mean, bins=30, color="b", alpha=0.5)

########################################################################################

plt.show()

##########################################################################################################

def type12_error():

x = np.linspace(-6, 9, 200)

null_loc, alter_loc = 0, 3

y_null = sp.stats.norm.pdf(x, loc=null_loc)

y_alter = sp.stats.norm.pdf(x, loc=alter_loc)

fig, ax = plt.subplots(figsize=(18, 6))

ax.plot(x, y_null, x, y_alter)

ax.annotate("Null", (null_loc - 0.2, max(y_null) / 2), size=15)

ax.annotate("Alternative", (alter_loc - 0.6, max(y_alter) / 2), size=15)

ax.annotate("Type I Error", (2, max(y_alter) / 30), size=15)

ax.annotate("Type II Error", (0, max(y_alter) / 30), size=15)

ax.fill_between(x[-98:], y_null[-98:])

ax.fill_between(x[:103], y_alter[:103])

ax.set_ylim([0, 0.5])

plt.show()

##########################################################################################################

# def reject_region():

# data = pd.read_csv('500_Person_Gender_Height_Weight_Index.csv')

# male_mean = data[data['Gender']=='Male']['Height'].mean()

# male_std = data[data['Gender']=='Male']['Height'].std(ddof=1)

# male_std_error = male_std/np.sqrt(len(data[data['Gender']=='Male']))

# male_null = 172

# df = len(data[data['Gender']=='Male'])-1

# t_975 = sp.stats.t.ppf(.975, df=df)

# t_025 = sp.stats.t.ppf(.025, df=df)

# x = np.linspace(male_null-5, male_null+5, 200)

# df = len(data[data['Gender']=='Male'])-1

# y_t = sp.stats.t.pdf(x, df = df, loc = male_null)

# fig, ax = plt.subplots(2, 1, figsize = (18,8))

# ax[0].plot(x, y_t, color = 'tomato', lw = 3)

# rejection_lower = male_null - t_975*male_std_error

# x_rej_lower = np.linspace(rejection_lower-3, rejection_lower, 30)

# y_rej_lower = sp.stats.t.pdf(x_rej_lower, df = df, loc = male_null)

# ax[0].fill_between(x_rej_lower, y_rej_lower, color = 'tomato', alpha = .7)

# rejection_upper = male_null + t_975*male_std_error

# x_rej_upper = np.linspace(rejection_upper, rejection_upper+3, 30)

# y_rej_upper = sp.stats.t.pdf(x_rej_upper, df = df, loc = male_null)

# ax[0].fill_between(x_rej_upper, y_rej_upper, color = 'tomato', alpha = .7)

# ax[0].set_ylim([0, .45])

# x = np.linspace(-5, 5, 200)

# y_t = sp.stats.t.pdf(x, df = df, loc = 0)

# ax[1].plot(x, y_t, color = 'tomato', lw = 3)

# x_rej_lower = np.linspace(t_025-3, t_025, 30)

# y_rej_lower = sp.stats.t.pdf(x_rej_lower, df = df)

# ax[1].fill_between(x_rej_lower, y_rej_lower, color = 'tomato', alpha = .7)

# x_rej_lower = np.linspace(t_975+3, t_975, 30)

# y_rej_lower = sp.stats.t.pdf(x_rej_lower, df = df)

# ax[1].fill_between(x_rej_lower, y_rej_lower, color = 'tomato', alpha = .7)

# ax[1].set_ylim([0, .45])

# plt.show()

##########################################################################################################

# ##########################################################################################################

# def draw_something():

# x = np.linspace(0, 10, 100)

# y = np.sin(x)

# plt.plot(x, y)

##########################################################################################################

def anova_plot():

def gen_3samples(loc1, loc2, loc3, scale1, scale2, scale3, size1, size2, size3):

F_statistic, p_value = [], []

for i in range(1000):

a = sp.stats.norm.rvs(loc1, scale1, size1)

b = sp.stats.norm.rvs(loc2, scale2, size3)

c = sp.stats.norm.rvs(loc3, scale3, size3)

F, p = sp.stats.f_oneway(a, b, c)

F_statistic.append(F)

p_value.append(p)

return F_statistic, p_value

fig, ax = plt.subplots(nrows=6, ncols=3, figsize=(17, 34))

mu1, mu2, mu3, sig1, sig2, sig3, size1, size2, size3 = [

10,

20,

30,

]

params = [mu1, mu2, mu3, sig1, sig2, sig3, size1, size2, size3]

F_statistic, p_value = gen_3samples(*params)

n, bins, patches = ax[0, 0].hist(F_statistic, bins=50)

F_critical = sp.stats.f.ppf(0.95, 2, size1 + size2 + size3 - 3)

textstr = "\n".join(

(

"$\mu_1, \mu_2, \mu_3 = {}, {}, {}$".format(mu1, mu2, mu3),

"$\sigma_1, \sigma_2, \sigma_3 = {}, {}, {}$".format(sig1, sig2, sig3),

"$n_1, n_2, n_3 = {}, {}, {}$".format(size1, size2, size3),

r"$F_c = {:.4f}$".format(F_critical),

)

props = dict(boxstyle="round", facecolor="wheat", alpha=0.5)

ax[0, 0].text(

max(bins) / 2,

max(n) / 2,

textstr,

fontsize=10,

verticalalignment="top",

bbox=props,

)

ax[0, 0].set_title("Simulation 1")

ax[0, 0].vlines(F_critical, 0, max(n) * 1.1, color="r")

ax[1, 0].hist(p_value, bins=50)

mu1, mu2, mu3, sig1, sig2, sig3, size1, size2, size3 = [

3.1,

2.9,

10,

20,

30,

]

params = [mu1, mu2, mu3, sig1, sig2, sig3, size1, size2, size3]

F_statistic, p_value = gen_3samples(*params)

n, bins, patches = ax[0, 1].hist(F_statistic, bins=50)

F_critical = sp.stats.f.ppf(0.95, 2, size1 + size2 + size3 - 3)

textstr = "\n".join(

(

"$\mu_1, \mu_2, \mu_3 = {}, {}, {}$".format(mu1, mu2, mu3),

"$\sigma_1, \sigma_2, \sigma_3 = {}, {}, {}$".format(sig1, sig2, sig3),

"$n_1, n_2, n_3 = {}, {}, {}$".format(size1, size2, size3),

r"$F_c = {:.4f}$".format(F_critical),

)

props = dict(boxstyle="round", facecolor="wheat", alpha=0.5)

ax[0, 1].text(

max(bins) / 2,

max(n) / 2,

textstr,

fontsize=10,

verticalalignment="top",

bbox=props,

)

ax[0, 1].vlines(F_critical, 0, max(n) * 1.1, color="r")

ax[1, 1].hist(p_value, bins=50)

ax[0, 1].set_title("Simulation 2")

mu1, mu2, mu3, sig1, sig2, sig3, size1, size2, size3 = [

3.1,

2.9,

12,

18,

10,

20,

30,

]

params = [mu1, mu2, mu3, sig1, sig2, sig3, size1, size2, size3]

F_statistic, p_value = gen_3samples(*params)

n, bins, patches = ax[0, 2].hist(F_statistic, bins=50)

F_critical = sp.stats.f.ppf(0.95, 2, size1 + size2 + size3 - 3)

textstr = "\n".join(

(

"$\mu_1, \mu_2, \mu_3 = {}, {}, {}$".format(mu1, mu2, mu3),

"$\sigma_1, \sigma_2, \sigma_3 = {}, {}, {}$".format(sig1, sig2, sig3),

"$n_1, n_2, n_3 = {}, {}, {}$".format(size1, size2, size3),

r"$F_c = {:.4f}$".format(F_critical),

)

props = dict(boxstyle="round", facecolor="wheat", alpha=0.5)

ax[0, 2].text(

max(bins) / 2,

max(n) / 2,

textstr,

fontsize=10,

verticalalignment="top",

bbox=props,

)

ax[0, 2].vlines(F_critical, 0, max(n) * 1.1, color="r")

ax[1, 2].hist(p_value, bins=50)

ax[0, 2].set_title("Simulation 3")

mu1, mu2, mu3, sig1, sig2, sig3, size1, size2, size3 = [

10,

20,

30,

]

params = [mu1, mu2, mu3, sig1, sig2, sig3, size1, size2, size3]

F_statistic, p_value = gen_3samples(*params)

n, bins, patches = ax[2, 0].hist(F_statistic, bins=50)

F_critical = sp.stats.f.ppf(0.95, 2, size1 + size2 + size3 - 3)

textstr = "\n".join(

(

"$\mu_1, \mu_2, \mu_3 = {}, {}, {}$".format(mu1, mu2, mu3),

"$\sigma_1, \sigma_2, \sigma_3 = {}, {}, {}$".format(sig1, sig2, sig3),

"$n_1, n_2, n_3 = {}, {}, {}$".format(size1, size2, size3),

r"$F_c = {:.4f}$".format(F_critical),

)

props = dict(boxstyle="round", facecolor="wheat", alpha=0.5)

ax[2, 0].text(

max(bins) / 2,

max(n) / 2,

textstr,

fontsize=10,

verticalalignment="top",

bbox=props,

)

ax[2, 0].vlines(F_critical, 0, max(n) * 1.1, color="r")

ax[3, 0].hist(p_value, bins=50)

ax[2, 0].set_title("Simulation 4")

mu1, mu2, mu3, sig1, sig2, sig3, size1, size2, size3 = [

10,

]

params = [mu1, mu2, mu3, sig1, sig2, sig3, size1, size2, size3]

F_statistic, p_value = gen_3samples(*params)

n, bins, patches = ax[2, 1].hist(F_statistic, bins=50)

F_critical = sp.stats.f.ppf(0.95, 2, size1 + size2 + size3 - 3)

textstr = "\n".join(

(

"$\mu_1, \mu_2, \mu_3 = {}, {}, {}$".format(mu1, mu2, mu3),

"$\sigma_1, \sigma_2, \sigma_3 = {}, {}, {}$".format(sig1, sig2, sig3),

"$n_1, n_2, n_3 = {}, {}, {}$".format(size1, size2, size3),

r"$F_c = {:.4f}$".format(F_critical),

)

props = dict(boxstyle="round", facecolor="wheat", alpha=0.5)

ax[2, 1].text(

max(bins) / 2,

max(n) / 2,

textstr,

fontsize=10,

verticalalignment="top",

bbox=props,

)

ax[2, 1].vlines(F_critical, 0, max(n) * 1.1, color="r")

ax[3, 1].hist(p_value, bins=50)

ax[2, 1].set_title("Simulation 5")

mu1, mu2, mu3, sig1, sig2, sig3, size1, size2, size3 = [

10,

5000,

]

params = [mu1, mu2, mu3, sig1, sig2, sig3, size1, size2, size3]

F_statistic, p_value = gen_3samples(*params)

n, bins, patches = ax[2, 2].hist(F_statistic, bins=50)

F_critical = sp.stats.f.ppf(0.95, 2, size1 + size2 + size3 - 3)

textstr = "\n".join(

(

"$\mu_1, \mu_2, \mu_3 = {}, {}, {}$".format(mu1, mu2, mu3),

"$\sigma_1, \sigma_2, \sigma_3 = {}, {}, {}$".format(sig1, sig2, sig3),

"$n_1, n_2, n_3 = {}, {}, {}$".format(size1, size2, size3),

r"$F_c = {:.4f}$".format(F_critical),

)

props = dict(boxstyle="round", facecolor="wheat", alpha=0.5)

ax[2, 2].text(

max(bins) / 2,

max(n) / 2,

textstr,

fontsize=10,

verticalalignment="top",

bbox=props,

)

ax[2, 2].vlines(F_critical, 0, max(n) * 1.1, color="r")

ax[3, 2].hist(p_value, bins=50)

ax[2, 2].set_title("Simulation 6")

mu1, mu2, mu3, sig1, sig2, sig3, size1, size2, size3 = [

100,

10,

]

params = [mu1, mu2, mu3, sig1, sig2, sig3, size1, size2, size3]

F_statistic, p_value = gen_3samples(*params)

n, bins, patches = ax[4, 0].hist(F_statistic, bins=50)

F_critical = sp.stats.f.ppf(0.95, 2, size1 + size2 + size3 - 3)

textstr = "\n".join(

(

"$\mu_1, \mu_2, \mu_3 = {}, {}, {}$".format(mu1, mu2, mu3),

"$\sigma_1, \sigma_2, \sigma_3 = {}, {}, {}$".format(sig1, sig2, sig3),

"$n_1, n_2, n_3 = {}, {}, {}$".format(size1, size2, size3),

r"$F_c = {:.4f}$".format(F_critical),

)

props = dict(boxstyle="round", facecolor="wheat", alpha=0.5)

ax[4, 0].text(

max(bins) / 2,

max(n) / 2,

textstr,

fontsize=10,

verticalalignment="top",

bbox=props,

)

ax[4, 0].vlines(F_critical, 0, max(n) * 1.1, color="r")

ax[5, 0].hist(p_value, bins=50)

ax[4, 0].set_title("Simulation 7")

mu1, mu2, mu3, sig1, sig2, sig3, size1, size2, size3 = [

10,

20,

30,

]

params = [mu1, mu2, mu3, sig1, sig2, sig3, size1, size2, size3]

F_statistic, p_value = gen_3samples(*params)

n, bins, patches = ax[4, 1].hist(F_statistic, bins=50)

F_critical = sp.stats.f.ppf(0.95, 2, size1 + size2 + size3 - 3)

textstr = "\n".join(

(

"$\mu_1, \mu_2, \mu_3 = {}, {}, {}$".format(mu1, mu2, mu3),

"$\sigma_1, \sigma_2, \sigma_3 = {}, {}, {}$".format(sig1, sig2, sig3),

"$n_1, n_2, n_3 = {}, {}, {}$".format(size1, size2, size3),

r"$F_c = {:.4f}$".format(F_critical),

)

props = dict(boxstyle="round", facecolor="wheat", alpha=0.5)

ax[4, 1].text(

max(bins) / 2,

max(n) / 2,

textstr,

fontsize=10,

verticalalignment="top",

bbox=props,

)

ax[4, 1].vlines(F_critical, 0, max(n) * 1.1, color="r")

ax[5, 1].hist(p_value, bins=50)

ax[4, 1].set_title("Simulation 8")

params = [3, 3.1, 2.9, 0.01, 0.01, 0.01, 10, 20, 30]

mu1, mu2, mu3, sig1, sig2, sig3, size1, size2, size3 = [

10,

20,

30,

]

params = [mu1, mu2, mu3, sig1, sig2, sig3, size1, size2, size3]

F_statistic, p_value = gen_3samples(*params)

n, bins, patches = ax[4, 2].hist(F_statistic, bins=50)

F_critical = sp.stats.f.ppf(0.95, 2, size1 + size2 + size3 - 3)

textstr = "\n".join(

(

"$\mu_1, \mu_2, \mu_3 = {}, {}, {}$".format(mu1, mu2, mu3),

"$\sigma_1, \sigma_2, \sigma_3 = {}, {}, {}$".format(sig1, sig2, sig3),

"$n_1, n_2, n_3 = {}, {}, {}$".format(size1, size2, size3),

r"$F_c = {:.4f}$".format(F_critical),

)

props = dict(boxstyle="round", facecolor="wheat", alpha=0.5)

ax[4, 2].text(

max(bins) / 2,

max(n) / 2,

textstr,

fontsize=10,

verticalalignment="top",

bbox=props,

)

ax[4, 2].vlines(F_critical, 0, max(n) * 1.1, color="r")

ax[5, 2].hist(p_value, bins=50)

ax[4, 2].set_title("Simulation 9")

#######################||Rectangle||##########################

##############################################################

rect = plt.Rectangle(

# (lower-left corner), width, height

(0.10, 0.633),

0.2645,

0.258,

fill=False,

color="k",

lw=2,

zorder=1000,

transform=fig.transFigure,

figure=fig,

)

fig.patches.extend([rect])

rect = plt.Rectangle(

# (lower-left corner), width, height

(0.3755, 0.633),

0.2645,

0.258,

fill=False,

color="k",

lw=2,

zorder=1000,

transform=fig.transFigure,

figure=fig,

)

fig.patches.extend([rect])

rect = plt.Rectangle(

# (lower-left corner), width, height

(0.650, 0.633),

0.2645,

0.258,

fill=False,

color="k",

lw=2,

zorder=1000,

transform=fig.transFigure,

figure=fig,

)

fig.patches.extend([rect])

rect = plt.Rectangle(

# (lower-left corner), width, height

(0.10, 0.37),

0.2645,

0.258,

fill=False,

color="k",

lw=2,

zorder=1000,

transform=fig.transFigure,

figure=fig,

)

fig.patches.extend([rect])

rect = plt.Rectangle(

# (lower-left corner), width, height

(0.3755, 0.37),

0.2645,

0.258,

fill=False,

color="k",

lw=2,

zorder=1000,

transform=fig.transFigure,

figure=fig,

)

fig.patches.extend([rect])

rect = plt.Rectangle(

# (lower-left corner), width, height

(0.650, 0.37),

0.2645,

0.258,

fill=False,

color="k",

lw=2,

zorder=1000,

transform=fig.transFigure,

figure=fig,

)

fig.patches.extend([rect])

rect = plt.Rectangle(

# (lower-left corner), width, height

(0.650, 0.108),

0.2645,

0.258,

fill=False,

color="k",

lw=2,

zorder=1000,

transform=fig.transFigure,

figure=fig,

)

fig.patches.extend([rect])

rect = plt.Rectangle(

# (lower-left corner), width, height

(0.3755, 0.108),

0.2645,

0.258,

fill=False,

color="k",

lw=2,

zorder=1000,

transform=fig.transFigure,

figure=fig,

)

fig.patches.extend([rect])

rect = plt.Rectangle(

# (lower-left corner), width, height

(0.1, 0.108),

0.2645,

0.258,

fill=False,

color="k",

lw=2,

zorder=1000,

transform=fig.transFigure,

figure=fig,

)

fig.patches.extend([rect])

####################################################################

plt.show()

###############################################################################################

def two_tail_rej_region_demo():

data = pd.read_csv("500_Person_Gender_Height_Weight_Index.csv")

df = len(data[data["Gender"] == "Male"]) - 1

t_975 = sp.stats.t.ppf(0.975, df=df)

t_025 = sp.stats.t.ppf(0.025, df=df)

male_mean = data[data["Gender"] == "Male"]["Height"].mean()

male_std = data[data["Gender"] == "Male"]["Height"].std(ddof=1)

male_std_error = male_std / np.sqrt(len(data[data["Gender"] == "Male"]))

male_null = 172

x = np.linspace(male_null - 5, male_null + 5, 200)

y_t = sp.stats.t.pdf(x, df=df, loc=male_null)

fig, ax = plt.subplots(2, 1, figsize=(18, 8))

ax[0].plot(x, y_t, color="tomato", lw=3)

rejection_lower = male_null - t_975 * male_std_error

x_rej_lower = np.linspace(rejection_lower - 3, rejection_lower, 30)

y_rej_lower = sp.stats.t.pdf(x_rej_lower, df=df, loc=male_null)

ax[0].fill_between(x_rej_lower, y_rej_lower, color="tomato", alpha=0.7)

rejection_upper = male_null + t_975 * male_std_error

x_rej_upper = np.linspace(rejection_upper, rejection_upper + 3, 30)

y_rej_upper = sp.stats.t.pdf(x_rej_upper, df=df, loc=male_null)

ax[0].fill_between(x_rej_upper, y_rej_upper, color="tomato", alpha=0.7)

ax[0].set_ylim([0, 0.45])

ax[0].set_title("Rejection Region of Original Unit (cm)")

x = np.linspace(-5, 5, 200)

y_t = sp.stats.t.pdf(x, df=df, loc=0)

ax[1].plot(x, y_t, color="tomato", lw=3)

x_rej_lower = np.linspace(t_025 - 3, t_025, 30)

y_rej_lower = sp.stats.t.pdf(x_rej_lower, df=df)

ax[1].fill_between(x_rej_lower, y_rej_lower, color="tomato", alpha=0.7)

x_rej_lower = np.linspace(t_975 + 3, t_975, 30)

y_rej_lower = sp.stats.t.pdf(x_rej_lower, df=df)

ax[1].fill_between(x_rej_lower, y_rej_lower, color="tomato", alpha=0.7)

ax[1].set_ylim([0, 0.45])

ax[1].set_title("Rejection Region of t-statistic")

plt.show()

###############################################################################################

def one_tail_rej_region_demo():

fig, ax = plt.subplots(2, 1, figsize=(18, 8))

x = np.linspace(-5, 5, 200)

y_t = sp.stats.t.pdf(x, df=len(x), loc=0)

ax[0].plot(x, y_t, color="tomato")

ax[0].annotate("$H_0: \mu = \mu_0$\n$H_1: \mu < \mu_0$", (-5, 0.35), size=16)

t_05 = sp.stats.t.ppf(0.05, df=len(x))

x_rej_lower = np.linspace(t_05, t_05 - 3, 30)

y_rej_lower = sp.stats.t.pdf(x_rej_lower, df=len(x))

ax[0].fill_between(x_rej_lower, y_rej_lower, color="tomato", alpha=0.7)

ax[0].set_ylim([0, 0.45])

x = np.linspace(-5, 5, 200)

y_t = sp.stats.t.pdf(x, df=len(x), loc=0)

ax[1].plot(x, y_t, color="tomato")

ax[1].annotate("$H_0: \mu = \mu_0$\n$H_1: \mu > \mu_0$", (4, 0.35), size=16)

t_95 = sp.stats.t.ppf(0.95, df=len(x))

x_rej_lower = np.linspace(t_95, t_95 + 3, 30)

y_rej_lower = sp.stats.t.pdf(x_rej_lower, df=len(x))

ax[1].fill_between(x_rej_lower, y_rej_lower, color="tomato", alpha=0.7)

ax[1].set_ylim([0, 0.45])

plt.show()

###############################################################################################

class Data:

def __init__(self, **kwargs):

"""Input start, end, database"""

self.__dict__.update(kwargs)

self.start = start

self.end = end

self.database = database

def retrieve(self, data_id):

if self.database == "fred":

self.df = pdr.data.DataReader(data_id, self.database, self.start, self.end)

elif self.database == "oecd":

self.df = pdr.data.DataReader(data_id, self.database)

elif self.database == "eurostat":

self.df = pdr.data.DataReader(data_id, self.database)

def normalise(self):

self.df_normalised = self.df / self.df.iloc[1]

def plot(self, labels, grid_on, norm):

if norm == False:

self.labels = labels

self.grid_on = grid_on

fig, ax = plt.subplots(figsize=(14, 8))

for col, label in zip(

self.df, self.labels

): # for drawing multiple labels/legends

ax.plot(self.df_normalised[col], label=label)

ax.grid(grid_on)

ax.legend()

plt.show()

else:

self.label = labels

self.grid_on = grid_on

fig, ax = plt.subplots(figsize=(14, 8))

for col, label in zip(self.df_normalised, self.label):

ax.plot(self.df_normalised[col], label=label)

ax.legend()

ax.grid(grid_on)

plt.show()

def twin_plot(

self, lhs, rhs, labels, grid_on, ax_rhs_inverse, lhs_color, rhs_color

self.lhs = lhs

self.rhs = rhs

self.labels = labels

self.grid_on = grid_on

self.ax_rhs_inverse = ax_rhs_inverse

self.lhs_color = lhs_color

self.rhs_color = rhs_color

fig, ax = plt.subplots(figsize=(14, 8))

ax.plot(self.df[self.lhs].dropna(), label=labels[0], color=self.lhs_color)

ax.legend(loc=3)

ax_RHS = ax.twinx() # share the same x-axis

ax_RHS.plot(self.df[self.rhs].dropna(), label=labels[1], color=self.rhs_color)

ax_RHS.legend(loc=0)

if ax_rhs_inverse == True:

ax_RHS.invert_yaxis()

ax.grid(grid_on)

plt.show()

Econometrics-With-Python/plot_material.py at main · weijie-chen/Econometrics-With-Python · GitHub

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