# -*- coding: utf-8 -*-
"""
Created on Sun Jan  9 10:26:00 2022

@author: Rene
"""

import numpy as np
import matplotlib.pyplot as plt

def h_1(Jury_Sample):
    n = len(Jury_Sample)
    value=(np.sum(Jury_Sample)-np.min(Jury_Sample)-np.max(Jury_Sample))/(n-2)
    return(value)

def h_2(Jury_Sample):
  value =  np.median(Jury_Sample)
  return(value)


N_Jurors= 7
Score = 8
jury_scores = np.repeat(Score,N_Jurors)
jury_scores = jury_scores + np.random.uniform(-0.5,0.5,N_Jurors,)
jury_scores
print(h_1(jury_scores))
print(h_2(jury_scores))

m = 1000
M = np.zeros(m)
T = np.zeros(m)
for i in np.arange(0,m):
  jury_scores = np.repeat(Score,N_Jurors)
  jury_scores = jury_scores + np.random.uniform(-0.5,0.5,N_Jurors,)
  T[i] = np.abs(h_1(jury_scores)-Score)
  M[i] = np.abs(h_2(jury_scores)-Score)

P_M_better = np.sum(M<T)/m

# 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=0.15, right=0.95, top=0.85, hspace=0.1, wspace=0.25)

#***************************************************************************************
LB_x = 0
UB_x = 0.5
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 = 0.5
off_set_y = 0.05*(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('$|T|$')
plt.ylabel('$|M|$')
text_str = r'Jury Rule Evaluation'
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.scatter(T,M,color='red',alpha = 0.5,s=5)

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

text_str = r'sample size = '+ f'{m:0.0f}'
plt.text(0.025,0.475,text_str,horizontalalignment = 'left',verticalalignment = 'center', color = 'red')

text_str = r'$T$ is better'
plt.text(0.025,0.425,text_str,horizontalalignment = 'left',verticalalignment = 'center', color = 'black')

text_str = r'$Pr(|M|>|T|) = $'+ f'{1-P_M_better:0.3f}'
plt.text(0.025,0.375,text_str,horizontalalignment = 'left',verticalalignment = 'center', color = 'black')

text_str = r'$M$ is better'
plt.text(0.475,0.125,text_str,horizontalalignment = 'right',verticalalignment = 'center', color = 'black')

text_str = r'$Pr(|M|<|T|) = $'+ f'{P_M_better:0.3f}'
plt.text(0.475,0.075,text_str,horizontalalignment = 'right',verticalalignment = 'center', color = 'black')

#***************************************************************************************
LB_x = -0.3
UB_x = 0.3
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 = 7
off_set_y = 0.05*(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('$|M|-|T|$')
plt.ylabel('Density')
text_str = r'Jury Rule Evaluation'
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.hist(M-T,density = 'True',color = 'red',alpha=0.5,edgecolor = 'black')

text_str = r'$M$ is better'
plt.text(-0.3,6.5,text_str,horizontalalignment = 'left',verticalalignment = 'center', color = 'black')

text_str = r'$Pr(|M|<|T|) = $'
plt.text(-0.3,6,text_str,horizontalalignment = 'left',verticalalignment = 'center', color = 'black')

text_str = f'{P_M_better:0.3f}'
plt.text(-0.3,5.5,text_str,horizontalalignment = 'left',verticalalignment = 'center', color = 'black')

text_str = r'$T$ is better'
plt.text(0.3,6.5,text_str,horizontalalignment = 'right',verticalalignment = 'center', color = 'black')

text_str = r'$Pr(|M|>|T|) = $'
plt.text(0.3,6,text_str,horizontalalignment = 'right',verticalalignment = 'center', color = 'black')

text_str = f'{1-P_M_better:0.3f}'
plt.text(0.3,5.5,text_str,horizontalalignment = 'right',verticalalignment = 'center', color = 'black')

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