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

@author: Rene
"""

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

the_lambda = 0.5
x = np.arange(0,101)/100
LB_x = 0
UB_x = 12
x = (UB_x-LB_x)*x+LB_x
pdf_exp = expon.pdf(x,scale = 1/the_lambda)
cdf_exp = expon.cdf(x,scale = 1/the_lambda)
pdf_gamma = gamma.pdf(x,a = 2,scale = 1/the_lambda)
cdf_gamma = gamma.cdf(x,a = 2,scale = 1/the_lambda)

# 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 = 10
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 = max(pdf_exp)
off_set_y = 0.05*(UB_y-LB_y)
y_lims = (LB_y-off_set_y,UB_y+off_set_y)

the_x = x
the_y = pdf_exp
plt.xlim(x_lims)
plt.ylim(y_lims)
plt.xlabel('x')
plt.ylabel('PDF $f(x)$')
title_str = r'PDF : $X \sim Exp(0.5)$'
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)
x_values = [2,2]
y_values = [0,expon.pdf(2,scale = 1/the_lambda)]
plt.plot(x_values,y_values, color='black', lw=1, ls=':')

# Adding a panel to the figure
Panel = Figure.add_subplot(2,2,2)  
LB_x = 0
UB_x = 10
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 = max(pdf_exp)
off_set_y = 0.05*(UB_y-LB_y)
y_lims = (LB_y-off_set_y,UB_y+off_set_y)

the_x = x
the_y = pdf_gamma
plt.xlim(x_lims)
plt.ylim(y_lims)
plt.xlabel('x')
plt.ylabel('PDF $f(x)$')
title_str = r'PDF : $X \sim Gamma(2,0.5)$'
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)
x_values = [4,4]
y_values = [0,gamma.pdf(4,a = 2,scale = 1/the_lambda)]
plt.plot(x_values,y_values, color='black', lw=1, ls=':')

# Adding a panel to the figure
Panel = Figure.add_subplot(2,2,3)  
LB_x = 0
UB_x = 10
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 = x
the_y = cdf_exp
plt.xlim(x_lims)
plt.ylim(y_lims)
plt.xlabel('x')
plt.ylabel('CDF $F(x) = Pr(X \leq x)$')
title_str = r'CDF : $X \sim Exp(0.5)$'
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.axhline(1, lw=2, ls = '--',color = 'lightgray',alpha=0.5)
plt.plot(the_x,the_y, color='blue', lw=1)
x_values = [2,2]
y_values = [0,expon.cdf(2,scale = 1/the_lambda)]
plt.plot(x_values,y_values, color='black', lw=1, ls=':')
x_values = [0,2]
y_values = [expon.cdf(2,scale = 1/the_lambda),expon.cdf(2,scale = 1/the_lambda)]
plt.plot(x_values,y_values, color='black', lw=1, ls=':')
text_str = f'{expon.cdf(2,scale = 1/the_lambda):4.3f}'
plt.text(0.25,expon.cdf(2,scale = 1/the_lambda),text_str,color = 'black', size = 8,horizontalalignment  = 'left', verticalalignment  = 'bottom')
    
# Adding a panel to the figure
Panel = Figure.add_subplot(2,2,4)  
LB_x = 0
UB_x = 10
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 = x
the_y = cdf_gamma
plt.xlim(x_lims)
plt.ylim(y_lims)
plt.xlabel('x')
plt.ylabel('CDF $F(x) = Pr(X \leq x)$')
title_str = r'CDF : $X \sim Gamma(2,0.5)$'
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)
x_values = [4,4]
y_values = [0,gamma.cdf(4,a = 2,scale = 1/the_lambda)]
plt.plot(x_values,y_values, color='black', lw=1, ls=':')
x_values = [0,4]
y_values = [gamma.cdf(4,a = 2,scale = 1/the_lambda),gamma.cdf(4,a = 2,scale = 1/the_lambda)]
plt.plot(x_values,y_values, color='black', lw=1, ls=':')
text_str = f'{gamma.cdf(4,a = 2,scale = 1/the_lambda):4.3f}'
plt.text(0.25,gamma.cdf(4,a = 2,scale = 1/the_lambda),text_str,color = 'black', size = 8,horizontalalignment  = 'left', verticalalignment  = 'bottom')

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