# -*- coding: utf-8 -*-
"""
Created on Tue Aug 31 18:37:42 2021

@author: Rene
"""

import numpy as np
import matplotlib.pyplot as plt
import Dist_Library as dl

p = 0.1
mu=-np.log(p)

# Number of hours
n = 30

# Generate m random samples from Poisson distribution and evaluate S and T Estimates
m = 500
X_bar = np.zeros(m)
Var_hat = np.zeros(m)
for i in np.arange(0,m):
  x = np.random.poisson(mu,n)
  mu_bar=np.mean(x)
  var_hat=np.var(x)
  X_bar[i]=mu_bar
  Var_hat[i]=var_hat
  
# Calculating the histogram data for the left panel
Number_of_bins = 20
LB = 0
UB = 5
bins = np.linspace(LB, UB, Number_of_bins+1) 
X_bar_hist_data = dl.Estimate_empirical_histogram_table(bins,X_bar) 
Var_hat_hist_data = dl.Estimate_empirical_histogram_table(bins,Var_hat)

# Plotting a two panel histogram plot of the durations
# the waiting times

plt.rc('font', family='serif', size='10')
plt.figure(figsize=(10, 5))
Hist_Figure = plt.figure()
Hist_Figure.subplots_adjust(hspace=0.4, wspace=0.4)
off_set_x = 0.25
off_set_y = 0.05
max_y = 2
x_lims = (LB-off_set_x,UB+off_set_x)
y_lims = (0-off_set_y,max_y+off_set_y)

# Adding the left panel with the histogram of Estimator S
hist_data = X_bar_hist_data
the_bounds = np.append(hist_data["LB"][0],hist_data["UB"])
the_density = np.append(0,hist_data["Bin PDF"])
Panel = Hist_Figure.add_subplot(1,2,1)
dl.add_pmf_density_hist_to_figure_panel(Panel,the_bounds,the_density,'indianred')
plt.axvline(0, lw=2, ls = '-',color = 'lightgray',alpha=0.5)
plt.axhline(0, lw=2, ls = '-',color = 'lightgray',alpha=0.5)
plt.xlim(x_lims)
plt.ylim(y_lims)
plt.xlabel('$\overline{x}$')
plt.ylabel('Density')

text_str = '# Bins = '+str(Number_of_bins)
plt.text(5-0.15,1.5,text_str,color = 'red',size = 10,horizontalalignment='right')

text_str = 'm = '+str(m)
plt.text(5-0.15,1.4,text_str,color = 'red',size = 10,horizontalalignment='right')

plt.axvline(mu, lw=1, ls = '--',color = 'black',alpha=0.5)
text_str = '$\mu$ = '+f'{mu:2.2f}'
plt.text(mu+0.15,max_y-0.15,text_str,color = 'blue',size = 10)

text_str = 'Estimator ' + '$\overline{X}$'
Panel.set_title(text_str)

# Adding the left panel with the histogram of Estimator S
hist_data = Var_hat_hist_data
the_bounds = np.append(hist_data["LB"][0],hist_data["UB"])
the_density = np.append(0,hist_data["Bin PDF"])
Panel = Hist_Figure.add_subplot(1,2,2)
dl.add_pmf_density_hist_to_figure_panel(Panel,the_bounds,the_density,'lightblue')
plt.axvline(0, lw=2, ls = '-',color = 'lightgray',alpha=0.5)
plt.axhline(0, lw=2, ls = '-',color = 'lightgray',alpha=0.5)
plt.xlim(x_lims)
plt.ylim(y_lims)
plt.xlabel('$s^2$')
plt.ylabel('Density')

text_str = '# Bins = '+str(Number_of_bins)
plt.text(5-0.15,1.5,text_str,color = 'red',size = 10,horizontalalignment='right')

text_str = 'm = '+str(m)
plt.text(5-0.15,1.4,text_str,color = 'red',size = 10,horizontalalignment='right')

plt.axvline(mu, lw=1, ls = '--',color = 'black',alpha=0.5)
text_str = '$\mu$ = '+f'{mu:2.2f}'
plt.text(mu+0.15,max_y-0.15,text_str,color = 'blue',size = 10)

text_str = 'Estimator ' + '$S^2$'
Panel.set_title(text_str)

plt.savefig("Hist_X_bar_Var.png", dpi=1200)