# -*- coding: utf-8 -*-
"""
Created on Wed Sep  1 16:30:23 2021

@author: Rene
"""
import numpy as np
from scipy.stats import norm
from scipy.stats import t
import matplotlib.pyplot as plt

def get_conf_int(x,alpha):
    n = len(x)
    x_bar = np.mean(x)
    st_dev_x_bar = np.std(x,ddof=1)/(n**0.5)
    half_width = t.ppf(1-(alpha),n-1)*st_dev_x_bar
    bounds = np.zeros(2)
    bounds[0] = -100000
    bounds[1] = x_bar+half_width
    return(bounds)

n = 10
the_mu = 0
the_sigma = 1
alpha = 0.10

x_points = np.linspace(0,1,100)
LB = the_mu-4*the_sigma
UB = the_mu+4*the_sigma
x_points = (UB-LB)*x_points+LB
y_points = norm.pdf(x_points,the_mu,the_sigma)

sample = np.random.normal(the_mu, the_sigma, size = n)
x_bar = np.mean(sample)
conf_bounds = get_conf_int(sample,alpha)
mu_in_conf = (conf_bounds[0] <= the_mu) and (conf_bounds[1] >= the_mu)

# Plotting the analysis results    
LB = -3
UB = 3
off_set_x = 0.25
off_set_y = 0.01
max_y = 0.4
    
# Setting the attributes for the Figure     
plt.rc('font', family='serif', size='10')
Figure = plt.figure()
plt.figure(figsize=(10, 5))
Figure.subplots_adjust(hspace=0.4, wspace=0.4)
x_lims = (LB-off_set_x,UB+off_set_x)
y_lims = (0-off_set_y,max_y+off_set_y)
plt.axvline(0, lw=2, ls = '-',color = 'lightgray',alpha=0.5)
plt.axhline(0, lw=2, ls = '-',color = 'lightgray',alpha=0.5)
plt.xlim(x_lims)
plt.ylim(y_lims)
plt.xlabel('x')
plt.ylabel('density')

plt.plot(x_points,y_points,ls='-',lw=0.5,label='N(0,1) pdf',color='blue')
x_values = [the_mu, the_mu]
y_values = [0, norm.pdf(the_mu,the_mu,the_sigma)]
plt.plot(x_values,y_values,lw=0.5,ls='--',color='blue',label = 'True Average ' + '$\mu$')
plt.scatter(sample,np.zeros(n),color="red", s = 10,label = 'sample')

if mu_in_conf:
    conf_color = 'green'
else:
    conf_color = 'red'
    
x_values = [conf_bounds[0], conf_bounds[1] ]
y_values = [0.1,0.1]
plt.plot(x_values,y_values,lw=1,ls='-',color=conf_color,label = 'Conf.Int')
head_length = 0.005 
x_values = [conf_bounds[1], conf_bounds[1] ]
y_values = [0.1-head_length,0.1+head_length]
plt.plot(x_values,y_values,lw=1,ls='-',color=conf_color)   
    
x_values = [x_bar, x_bar]
y_values = [0, 0.1]
plt.plot(x_values,y_values,lw=0.5,ls='--',color='black')
text_str = '$\overline{x}$'
plt.text(x_bar,0.11,text_str)

text_str = 'Sample Size = ' +str(n)
plt.text(-3,0.35,text_str,color='red')

plt.legend(loc = 'best')

text_str = "Sampled " + f'{(100*(1-alpha)):2.0f}' + " % confidence interval - variance known"
Figure.suptitle(text_str,size='14')
plt.savefig('Confidence_Interval_Var_Unknown.png', dpi=1200)

text_str = "Sampled " + f'{(100*(1-alpha)):2.0f}' + " % confidence interval - variance known"
Figure.suptitle(text_str,size='14')
plt.savefig('Lower_Confidence_Interval_Var_Unknown.png', dpi=300)