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

@author: Rene
"""
import numpy as np
import matplotlib.pyplot as plt

def running_average(sample):
  n = len(sample)  
  r_average=np.zeros(n)
  sum = 0
  for i in np.arange(0,n):
      sum = sum+sample[i]
      r_average[i] = sum/(i+1)
  return(r_average)

m = 500

x_0 = 2
random_cauchy = np.random.standard_cauchy(m)
random_cauchy = random_cauchy + x_0
r_ave_cauchy = running_average(random_cauchy)

median_pareto = 2
alpha = 0.9
x_m = median_pareto/(2**(1/alpha))
random_pareto = np.random.pareto(alpha, m)
random_pareto = random_pareto+ x_m
r_ave_pareto = running_average(random_pareto)

mu = 2
sigma = 3
mean_normal = mu
random_normal = np.random.normal(mu,sigma,m)
r_ave_normal = running_average(random_normal)


# 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(2,2,1)  
LB_x = 0
UB_x = m
off_set_x = 0.025*(UB_x-LB_x)
x_lims = (LB_x-off_set_x,UB_x+off_set_x)
LB_y = -20
UB_y = 20
off_set_y = 0.05*(UB_y-LB_y)
y_lims = (LB_y-off_set_y,UB_y+off_set_y)

the_x = np.arange(0,m)
the_y = random_cauchy
plt.xlim(x_lims)
plt.ylim(y_lims)
plt.xlabel('k')
plt.ylabel('Random Sample')
title_str = r'$Cauchy[2,1]-Sample$'
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.scatter(the_x,the_y, color='red', s=1)
plt.axhline(x_0, lw=2, ls = '--',color = 'black',alpha=0.5)


# Adding a panel to the figure
Panel = Figure.add_subplot(2,2,2)  
LB_x = 0
UB_x = m
off_set_x = 0.025*(UB_x-LB_x)
x_lims = (LB_x-off_set_x,UB_x+off_set_x)
LB_y = 1
UB_y = 3
off_set_y = 0.05*(UB_y-LB_y)
y_lims = (LB_y-off_set_y,UB_y+off_set_y)

the_x = np.arange(0,m)
the_y = r_ave_cauchy
plt.xlim(x_lims)
plt.ylim(y_lims)
plt.xlabel('k')
plt.ylabel('Running Average')
title_str = r'$Cauchy[2,1]-Sample$'
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.axhline(x_0, lw=2, ls = '--',color = 'black',alpha=0.5)

# Adding a panel to the figure
Panel = Figure.add_subplot(2,2,3)  
LB_x = 0
UB_x = m
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 = 20
off_set_y = 0.05*(UB_y-LB_y)
y_lims = (LB_y-off_set_y,UB_y+off_set_y)

the_x = np.arange(0,m)
the_y = random_pareto
plt.xlim(x_lims)
plt.ylim(y_lims)
plt.xlabel('k')
plt.ylabel('Random Sample')
title_str = r'$Pareto[0.93,0.9]-Sample$'
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.scatter(the_x,the_y, color='blue',s=1)
plt.axhline(mean_normal, lw=2, ls = '--',color = 'black',alpha=0.5)

# Adding a panel to the figure
Panel = Figure.add_subplot(2,2,4)  
LB_x = 0
UB_x = m
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 = 20
off_set_y = 0.05*(UB_y-LB_y)
y_lims = (LB_y-off_set_y,UB_y+off_set_y)

the_x = np.arange(0,m)
the_y = r_ave_pareto
plt.xlim(x_lims)
plt.ylim(y_lims)
plt.xlabel('k')
plt.ylabel('Running Average')
title_str = r'$Pareto[0.93,0.9]-Sample$'
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='blue', lw=1)
plt.axhline(mean_normal, lw=2, ls = '--',color = 'black',alpha=0.5)

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