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

@author: Rene
"""

import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import uniform
from scipy.stats import expon
from scipy.stats import norm

def Chebishev_LB(a,sigma):
    value=1-(1/a**2)*sigma**2
    return(value)

x = np.zeros(100)
alpha = np.linspace(0,1,100)
LB_alpha = 1
UB_alpha = 6
alpha = (UB_alpha-LB_alpha)*alpha+LB_alpha
sigma = 1
CB_a = alpha*sigma
Cheb_LB = Chebishev_LB(CB_a,sigma)

a = 0
b = 1
mean_unif = (a+b)/2
var_unif = (b-a)**2/12
sd_unif = var_unif**0.5
hw_unif = alpha*sd_unif
UB = mean_unif+hw_unif
LB = mean_unif-hw_unif
Pr_unif = uniform.cdf(UB,a,b)-uniform.cdf(LB,a,b)

the_lambda = 1
mean_exp = 1/the_lambda
sd_exp = 1/the_lambda
hw_exp = alpha*sd_exp
UB = mean_exp+hw_exp
LB = mean_exp-hw_exp
Pr_exp = expon.cdf(UB,the_lambda)-expon.cdf(LB,the_lambda)

mu = 0
sigma = 1
mean_norm = mu
sd_norm = sigma
hw_norm = alpha*sd_norm
UB = mean_norm+hw_norm
LB = mean_norm-hw_norm
Pr_norm = norm.cdf(UB,mu,sigma)-norm.cdf(LB,mu,sigma)


# 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(1,1,1)  
LB_x = LB_alpha
UB_x = UB_alpha-1
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 = CB_a
the_y = Cheb_LB
plt.xlim(x_lims)
plt.ylim(y_lims)
x_str = r'$\alpha$'
plt.xlabel(x_str)
y_str = r'$\Pr(|Y-\mu|) < \alpha \cdot \sigma$'
plt.ylabel(y_str, size = 10)
title_str="Graphical Depiction of Chebishev's inequality"
plt.title(title_str, size = 12)
plt.axvline(1, lw=2, ls = '--',color = 'lightgray',alpha=0.5)
plt.axhline(0, lw=2, ls = '-',color = 'lightgray',alpha=0.5)
plt.axhline(1, lw=2, ls = '--',color = 'lightgray',alpha=0.5)
plt.plot(the_x,the_y, color='red', lw=1,label = 'Chebishev LB')
plt.plot(the_x,Pr_unif, color='green', lw=1,label = 'Unif[0,1]')
plt.plot(the_x,Pr_exp, color='blue', lw=1,label = 'Exp[1]')
plt.plot(the_x,Pr_norm, color='orange', lw=1,label = 'Normal[0,1]')

plt.fill_between(the_x, x, the_y, color = 'lightcyan', label = 'INFEASIBLE')

k = 2
y_k = Chebishev_LB(k,sigma)
x_values = [k,k]
y_values = [0,y_k]
plt.plot(x_values,y_values, color='black', lw=1, ls=':')
text_str = f'{y_k:2.2f}'
plt.text(k,y_k+0.025,text_str,color = 'black', size = 10,horizontalalignment  = 'center', verticalalignment  = 'bottom')

k = 3
y_k = Chebishev_LB(k,sigma)
x_values = [k,k]
y_values = [0,y_k]
plt.plot(x_values,y_values, color='black', lw=1, ls=':')
text_str = f'{y_k:2.2f}'
plt.text(k,y_k+0.025,text_str,color = 'black', size = 10,horizontalalignment  = 'center', verticalalignment  = 'bottom')

k = 4
y_k = Chebishev_LB(k,sigma)
x_values = [k,k]
y_values = [0,y_k]
plt.plot(x_values,y_values, color='black', lw=1, ls=':')
text_str = f'{y_k:2.2f}'
plt.text(k,y_k+0.025,text_str,color = 'black', size = 10,horizontalalignment  = 'center', verticalalignment  = 'bottom')

k = 5
y_k = Chebishev_LB(k,sigma)
x_values = [k,k]
y_values = [0,y_k]
plt.plot(x_values,y_values, color='black', lw=1, ls=':')
text_str = f'{y_k:2.2f}'
plt.text(k,y_k+0.025,text_str,color = 'black', size = 10,horizontalalignment  = 'center', verticalalignment  = 'bottom')

plt.legend(loc='best')

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