# -*- coding: utf-8 -*-
"""
Created on Wed Mar  4 18:10:08 2020

@author: Johan Rene van Dorp
"""
import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import uniform
from scipy.stats import expon
from scipy.stats import norm

a = 0
b = 1/3
unif_x = np.linspace(-1,2,1000,endpoint=True)
unif_cdf = uniform.cdf(unif_x,a,b)

lb = 0
ub = 21
the_lambda = 0.25
exp_x = np.linspace(lb,ub,1000,endpoint=True)
exp_pdf =  expon.pdf(exp_x, loc = 0, scale = 1/the_lambda)
exp_cdf =  expon.cdf(exp_x, loc = 0, scale = 1/the_lambda)

lb= -4
ub = 10
the_mu = 3
the_sigma = 2.5
norm_x = np.linspace(lb,ub,1000,endpoint=True)
norm_pdf =  norm.pdf(norm_x, loc = the_mu, scale = the_sigma)
norm_cdf =  norm.cdf(norm_x, loc = the_mu, scale = the_sigma)

# Plotting the Uniform PDF and CDF

plt.rc('font', family='serif', size='12')
Figure = plt.figure(1)
Figure.set_figwidth(9)
Figure.set_figheight(5)
Figure.subplots_adjust(left=0.1, bottom=0.1, right=0.95, top=0.85, hspace=0.1, wspace=0.25)

#***************************************************************************************

# Adding the left panel with the theoretical pmf
LB_x = -0.5
UB_x = 1
off_set_x = 0.05*(UB_x-LB_x)
x_lims = (LB_x-off_set_x,UB_x+off_set_x)

LB_y = 0
UB_y = 3.0
off_set_y = 0.1*(UB_y-LB_y)
y_lims = (LB_y-off_set_y,UB_y+off_set_y)

Panel = Figure.add_subplot(1,2,1)
plt.xlim(x_lims)
plt.ylim(y_lims)
plt.xlabel('x')
plt.ylabel('Probability Density Function $f(x)$')

text_str = r'PDF - Uniform $U[0,\frac{1}{3}]$'
plt.title(text_str)
plt.axvline(0, lw=2, ls = '-',color = 'lightgray',alpha=0.5)
plt.axhline(0, lw=2, ls = '-',color = 'lightgray',alpha=0.5)

x_values = [-1, a]
y_values = [0, 0]
plt.plot(x_values, y_values,color='red')

x_values = [a, b]
y_values = [1/(b-a), 1/(b-a)]
plt.plot(x_values, y_values,color='red')

x_values = [b, 2]
y_values = [0, 0]
plt.plot(x_values, y_values,color='red')

x_values = [0, 0]
y_values = [0, 1/(b-a)]
plt.plot(x_values, y_values,color='black',linestyle=':')

x_values = [b, b]
y_values = [0, 1/(b-a)]
plt.plot(x_values, y_values,color='black',linestyle=':')

text_str = r'$\frac{1}{3}$'
plt.text(b+0.05,0.25,text_str,horizontalalignment = 'left',verticalalignment = 'center')

# Adding the right panel with the empirical pmf
LB_x = -0.5
UB_x = 1
off_set_x = 0.05*(UB_x-LB_x)
x_lims = (LB_x-off_set_x,UB_x+off_set_x)
LB_y = 0
UB_y = 1
off_set_y = 0.1*(UB_y-LB_y)
y_lims = (LB_y-off_set_y,UB_y+off_set_y)

Panel = Figure.add_subplot(1,2,2)
plt.xlim(x_lims)
plt.ylim(y_lims)
plt.xlabel('x')
plt.ylabel('Cumulative Distribution Function $F(x)$')
text_str = r'CDF - Uniform $U[0,\frac{1}{3}]$'
plt.title(text_str)
plt.axvline(0, lw=2, ls = '-',color = 'lightgray',alpha=0.5)
plt.axhline(0, lw=2, ls = '-',color = 'lightgray',alpha=0.5)
plt.axhline(1, lw=1, ls = '--',color = 'darkgray',alpha=0.5)

plt.plot(unif_x,unif_cdf,color='red')
x_values = [b, b]
y_values = [0, 1]
plt.plot(x_values, y_values,color='black',linestyle=':')

text_str = r'$\frac{1}{3}$'
plt.text(b+0.05,0.25/(1/(b-a)),text_str,horizontalalignment = 'left',verticalalignment = 'center')

plt.savefig('Uniform_Example.png', dpi=300)

#Plotting the Exponential PDF and CDF

plt.rc('font', family='serif', size='12')
Figure = plt.figure(2)
Figure.set_figwidth(9)
Figure.set_figheight(5)
Figure.subplots_adjust(left=0.1, bottom=0.1, right=0.95, top=0.85, hspace=0.1, wspace=0.25)

#***************************************************************************************

# Adding the left panel with the theoretical pmf
LB_x = -5
UB_x = 20
off_set_x = 0.05*(UB_x-LB_x)
x_lims = (LB_x-off_set_x,UB_x+off_set_x)

LB_y = 0
UB_y = 0.25
off_set_y = 0.1*(UB_y-LB_y)
y_lims = (LB_y-off_set_y,UB_y+off_set_y)

Panel = Figure.add_subplot(1,2,1)
plt.xlim(x_lims)
plt.ylim(y_lims)
plt.xlabel('x')
plt.ylabel('Probability Density Function $f(x)$')

text_str = r'PDF - $Exp(\lambda)$, $\lambda = \frac{1}{4}$'
plt.title(text_str)
plt.axvline(0, lw=2, ls = '-',color = 'lightgray',alpha=0.5)
plt.axhline(0, lw=2, ls = '-',color = 'lightgray',alpha=0.5)

x_values = [-6, 0]
y_values = [0, 0]
plt.plot(x_values, y_values,color='red')

plt.plot(exp_x, exp_pdf,color='red')

x_values = [0, 0]
y_values = [0, the_lambda]
plt.plot(x_values, y_values,color='black',linestyle=':')

# Adding the right panel with the empirical pmf
LB_x = -5
UB_x = 20
off_set_x = 0.05*(UB_x-LB_x)
x_lims = (LB_x-off_set_x,UB_x+off_set_x)
LB_y = 0
UB_y = 1
off_set_y = 0.1*(UB_y-LB_y)
y_lims = (LB_y-off_set_y,UB_y+off_set_y)

Panel = Figure.add_subplot(1,2,2)
plt.xlim(x_lims)
plt.ylim(y_lims)
plt.xlabel('x')
plt.ylabel('Cumulative Distribution Function $F(x)$')
text_str = r'CDF - $Exp(\lambda)$, $\lambda = \frac{1}{4}$'
plt.title(text_str)
plt.axvline(0, lw=2, ls = '-',color = 'lightgray',alpha=0.5)
plt.axhline(0, lw=2, ls = '-',color = 'lightgray',alpha=0.5)
plt.plot(exp_x,exp_cdf,color='red')
plt.axhline(1, lw=1, ls = '--',color = 'darkgray',alpha=0.5)

x_values = [-6, 0]
y_values = [0, 0]
plt.plot(x_values, y_values,color='red')

plt.savefig('Exponential_Example.png', dpi=300)

#Plotting the Normal PDF and CDF

plt.rc('font', family='serif', size='12')
Figure = plt.figure(3)
Figure.set_figwidth(9)
Figure.set_figheight(5)
Figure.subplots_adjust(left=0.1, bottom=0.1, right=0.95, top=0.85, hspace=0.1, wspace=0.25)

#***************************************************************************************

# Adding the left panel with the normal pdf
LB_x = -3
UB_x = 9
off_set_x = 0.05*(UB_x-LB_x)
x_lims = (LB_x-off_set_x,UB_x+off_set_x)

LB_y = 0
UB_y = 0.2
off_set_y = 0.1*(UB_y-LB_y)
y_lims = (LB_y-off_set_y,UB_y+off_set_y)

Panel = Figure.add_subplot(1,2,1)
plt.xlim(x_lims)
plt.ylim(y_lims)
plt.xlabel('x')
plt.ylabel('Probability Density Function $f(x)$')

text_str = r'PDF - $N(\mu,\sigma)$, $\mu =3, \sigma = 2.5$'
plt.title(text_str)
plt.axvline(0, lw=2, ls = '-',color = 'lightgray',alpha=0.5)
plt.axhline(0, lw=2, ls = '-',color = 'lightgray',alpha=0.5)

plt.plot(norm_x, norm_pdf,color='red')

x_values = [the_mu, the_mu]
y_values = [0, norm.pdf(the_mu, loc = the_mu, scale = the_sigma)]
plt.plot(x_values, y_values,color='black',ls=':')

text_str = r'3'
plt.text(the_mu+0.1,0.01,text_str,horizontalalignment = 'left',verticalalignment = 'center')

# Adding the right panel with the normal cdf
LB_x = -3
UB_x = 9
off_set_x = 0.05*(UB_x-LB_x)
x_lims = (LB_x-off_set_x,UB_x+off_set_x)
LB_y = 0
UB_y = 1
off_set_y = 0.1*(UB_y-LB_y)
y_lims = (LB_y-off_set_y,UB_y+off_set_y)

Panel = Figure.add_subplot(1,2,2)
plt.xlim(x_lims)
plt.ylim(y_lims)
plt.xlabel('x')
plt.ylabel('Cumulative Distribution Function $F(x)$')
text_str = r'PDF - $N(\mu,\sigma)$, $\mu =3, \sigma = 2.5$'
plt.title(text_str)
plt.axvline(0, lw=2, ls = '-',color = 'lightgray',alpha=0.5)
plt.axhline(0, lw=2, ls = '-',color = 'lightgray',alpha=0.5)
plt.plot(norm_x,norm_cdf,color='red')
plt.axhline(1, lw=1, ls = '--',color = 'darkgray',alpha=0.5)

x_values = [the_mu, the_mu]
y_values = [0, 1]
plt.plot(x_values, y_values,color='black',ls=':')

text_str = r'3'
plt.text(the_mu+0.1,0.01/0.20,text_str,horizontalalignment = 'left',verticalalignment = 'center')

plt.savefig('Normal_Example.png', dpi=300)