# -*- coding: utf-8 -*-
"""
Created on Thu Mar 12 12:40:01 2020

@author: Johan Rene van Dorp
"""
import Dist_Library as dl
import numpy as np
import matplotlib.pyplot as plt

data = np.array([6,8,9,10,11,12,14,16,19,24])
data.sort()
print(data)
n = len(data)
F = np.arange(1,n+1)/n
print(F)

q_level = 0.85
x_q,k,x_k,x_k_plus_1 = dl.empirical_quantile(data,q_level)

print(x_k)
print(x_q)
print(x_k_plus_1)

# Parameters for the plots
LB_x = 0
UB_x = 25
LB_y = 0
UB_y = 1

data_appended = data
F_appended = F
data_appended = np.append(0,data_appended)
data_appended = np.append(data_appended,30)
print(data_appended)
F_appended = np.append(0,F_appended)
F_appended = np.append(F_appended,1)
print(F_appended)

plt.rc('font', family='serif', size='10')
plt.figure(figsize=(10, 5))
Q_Figure = plt.figure()
Q_Figure.set_figwidth(5)
Q_Figure.set_figheight(5)
Q_Figure.subplots_adjust(hspace=0.4, wspace=0.4)
#plt.rcParams['xtick.labelsize'] = 5
#plt.rcParams['ytick.labelsize'] = 5
off_set_x = 6
off_set_y = 0.05
x_lims = (LB_x-off_set_x,UB_x+off_set_x)
y_lims = (LB_y-off_set_y,UB_y+off_set_y)

Panel = Q_Figure.add_subplot(1,1,1)
plt.xlim(x_lims)
plt.ylim(y_lims)
plt.xlabel('x',size = '10')
plt.ylabel('Empirical CDF $\hat{F}(t) = Pr(T \leq t)$',size = '10')
plt.axvline(0, lw=1, ls = '-',color = 'lightgray',alpha=0.5)
plt.axhline(0, lw=1, ls = '-',color = 'lightgray',alpha=0.5)
plt.axhline(1, lw=1, ls = ':',color = 'lightgray',alpha=0.5)
plt.scatter(data,F,color = "navy", s = 10,alpha=0.5)
plt.plot(data_appended,F_appended,color = "red",lw=1,alpha=0.5)

plt.vlines(x_k, 0, k/n, color='black', linestyles='--', lw=1)
plt.vlines(x_q, 0, q_level, color='black', linestyles=':', lw=1)
plt.vlines(x_k_plus_1, 0, (k+1)/n, color='black', linestyles='--', lw=1)

plt.hlines(k/n, 0, x_k, color='black', linestyles='--', lw=1)
plt.hlines(q_level, 0, x_q, color='black', linestyles=':', lw=1)
plt.hlines((k+1)/n, 0, x_k_plus_1, color='black', linestyles='--', lw=1)

text_str = '$x_{(k)}$ =' + str(x_k)
plt.text(x_k-1, 0.1,text_str,color = 'red',horizontalalignment = 'right')

text_str = '$x_p$ =' + f'{x_q:4.2f}'
plt.text(x_q, 0.025,text_str,color = 'blue',horizontalalignment = 'center')

text_str = '$p$ =' + f'{q_level:4.2f}'
plt.text(-0.25, q_level,text_str,color = 'blue',horizontalalignment = 'right', verticalalignment = 'center')

text_str = '$x_{(k+1)}$ =' + str(x_k_plus_1)
plt.text(x_k_plus_1+1, 0.1, text_str, color = 'red',horizontalalignment = 'left')

Q_Figure.suptitle('Empirical Quantile - Linear Interpolation',size='14')
plt.savefig('Empirical_Quantile.png', dpi=300)