# -*- coding: utf-8 -*-
"""
Created on Thu Feb  3 18:47:48 2022

@author: Rene
"""

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import norm

x = np.arange(0,1001)/1000
LB_x = -30
UB_x = 300
x = (UB_x-LB_x)*x+LB_x
pdf_normal_3 = norm.pdf(x,loc=3,scale = 4)
cdf_normal_3 = norm.cdf(x,loc=3,scale = 4)
pdf_normal_5 = norm.pdf(x,loc=5,scale = 3)
cdf_normal_5 = norm.cdf(x,loc=5,scale = 3)
pdf_normal_8 = norm.pdf(x,loc=8,scale = 5)
cdf_normal_8 = norm.cdf(x,loc=8,scale = 5)

# Plotting a four panel figure

plt.rc('font', family='serif', size='10')
plt.figure(figsize=(10, 5))
Figure = plt.figure(0)
Figure.set_figwidth(9)
Figure.set_figheight(4.75)
Figure.subplots_adjust(hspace=0.5, wspace=0.25)

# Adding a panel to the figure
Panel = Figure.add_subplot(1,2,1)  
LB_x = -15
UB_x = 30
off_set_x = 0.025*(UB_x-LB_x)
x_lims = (LB_x-off_set_x,UB_x+off_set_x)
LB_y = 0
UB_y = max(pdf_normal_5)
off_set_y = 0.05*(UB_y-LB_y)
y_lims = (LB_y-off_set_y,UB_y+off_set_y)

the_x = x
the_y = pdf_normal_3
plt.xlim(x_lims)
plt.ylim(y_lims)
plt.xlabel('x ')
plt.ylabel('PDF $f(x)$')
title_str = r'PDF : Normal Distributions'
plt.title(title_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(the_x,the_y, color='red', lw=1)
plt.plot(the_x,pdf_normal_5, color='green', lw=1)
plt.plot(the_x,pdf_normal_8, color='blue', lw=1)

x_values = [3,3]
y_values = [0,norm.pdf(3,loc=3,scale = 4)]
plt.plot(x_values,y_values, color='black', lw=1, ls=':')

x_values = [5,5]
y_values = [0,norm.pdf(5,loc=5,scale = 3)]
plt.plot(x_values,y_values, color='black', lw=1, ls=':')

x_values = [8,8]
y_values = [0,norm.pdf(8,loc=8,scale = 5)]
plt.plot(x_values,y_values, color='black', lw=1, ls=':')

# Adding a panel to the figure
Panel = Figure.add_subplot(1,2,2)  
LB_x = -15
UB_x = 30
off_set_x = 0.025*(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 = 0.05*(UB_y-LB_y)
y_lims = (LB_y-off_set_y,UB_y+off_set_y)

the_x = x
the_y = cdf_normal_3
plt.xlim(x_lims)
plt.ylim(y_lims)
plt.xlabel('x')
plt.ylabel('CDF $F(x) = Pr(X\leq x)$')
title_str = r'CDF : Normal Distributions'
plt.title(title_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(the_x,the_y, color='red', lw=1)
plt.plot(the_x,cdf_normal_5, color='green', lw=1)
plt.plot(the_x,cdf_normal_8, color='blue', lw=1)

x_values = [3,3]
y_values = [0,norm.cdf(3,loc=3,scale = 4)]
plt.plot(x_values,y_values, color='black', lw=1, ls=':')

x_values = [0,3]
y_values = [norm.cdf(3,loc=3,scale = 4),norm.cdf(3,loc=3,scale = 4)]
plt.plot(x_values,y_values, color='black', lw=1, ls=':')

x_values = [5,5]
y_values = [0,norm.cdf(5,loc=5,scale = 3)]
plt.plot(x_values,y_values, color='black', lw=1, ls=':')

x_values = [0,5]
y_values = [norm.cdf(5,loc=5,scale = 3),norm.cdf(5,loc=5,scale = 3)]
plt.plot(x_values,y_values, color='black', lw=1, ls=':')

x_values = [8,8]
y_values = [0,norm.cdf(8,loc=8,scale = 5)]
plt.plot(x_values,y_values, color='black', lw=1, ls=':')

x_values = [0,8]
y_values = [norm.cdf(8,loc=8,scale = 5),norm.cdf(8,loc=8,scale = 5)]
plt.plot(x_values,y_values, color='black', lw=1, ls=':')

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