# -*- coding: utf-8 -*-
"""
Created on Sat Jan  8 15:19:57 2022

@author: Rene
"""

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

# Evaluating cdf of the uniform distribution on the interval [a,b]
the_lambda=2
expon_x = np.linspace(-1,4,1000,endpoint=True)
expon_cdf = expon.cdf(expon_x,scale = 1/the_lambda)

# Sampling from a Exponential Distribution with parameter lambda = 2
m = 100
sample = np.random.exponential(scale = 1/the_lambda,size = m)

# Transforming the Uniform Sample to a discrete distribution Sample
x_points = [0.25,0.75,1.25]
y_points = np.zeros(3)
y_points = expon.cdf(x_points,scale = 1/the_lambda)

y_points_emp = np.zeros(3)
y_points_emp[0] = len(sample[sample <= x_points[0]])/m
y_points_emp[1] = len(sample[sample <= x_points[1]])/m
y_points_emp[2] = len(sample[sample <= x_points[2]])/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=0.1, right=0.95, top=0.85, hspace=0.1, wspace=0.25)

#***************************************************************************************
LB_x = 0
UB_x = 2.5
off_set_x = 0.1*(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 = 0.1*(UB_y-LB_y)
y_lims = (LB_y-off_set_y,UB_y+off_set_y)

Panel = Figure.add_subplot(1,1,1)
plt.xlim(x_lims)
plt.ylim(y_lims)
plt.xlabel('x')
plt.ylabel('Cumulative Distribution Function $F(x)$')
text_str = r'CDF - $Exp(\lambda)$, $\lambda = 2$'
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.plot(expon_x,expon_cdf,color='red',alpha = 0.5)
plt.scatter(x_points,y_points,color = 'green',alpha=0.5,s=100)
plt.scatter(x_points,y_points_emp,color = 'blue')

text_str = r'sample size = '+ f'{m:0.0f}'
plt.text(0.025,0.95,text_str,horizontalalignment = 'left',verticalalignment = 'center', color = 'red')

for i in np.arange(0,3):
    text_str = f'{y_points[i]:0.2f}'
    plt.text(x_points[i]+0.05,y_points[i],text_str,horizontalalignment = 'left',verticalalignment = 'center', color = 'green')
    
    x_values = [x_points[i], x_points[i]]
    y_values = [0, y_points_emp[i]]
    plt.plot(x_values, y_values,color='blue')
    
    text_str = r'$\widehat{p} = $'+ f'{y_points_emp[i]:0.3f}'
    plt.text(x_points[i]-0.05,y_points_emp[i],text_str,horizontalalignment = 'right',verticalalignment = 'center', color = 'blue')
    
    

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