# -*- coding: utf-8 -*-
"""
Created on Fri Sep 10 16:59:10 2021

@author: Rene
"""

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


df = pd.read_csv('BallBearings.csv')
Diameter = df["Diameter"]

# H_0: mu = mu_0  H_1: mu not = mu_0

mu_0 = 1
n = len(Diameter)
s_n = np.std(Diameter,ddof=1)
x_bar = np.mean(Diameter)

# Assuming H_0 is True and with estimate for sigma evaluating theoretical pdf

LB = mu_0-5*s_n
UB = mu_0+5*s_n
x_points = np.linspace(LB,UB,1000)
y_points = norm.pdf(x_points,mu_0,s_n)

off_set_x = 0
off_set_y = 0.5
max_y = 12

# Comparing dataset with the theoretical pdf and mu_0 with x_bar

# Setting the attributes for the Figure     
plt.rc('font', family='serif', size='10')
Figure = plt.figure()
Figure.set_figwidth(9)
Figure.set_figheight(4.25)
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,color='blue',label = '$X \sim N(\mu,\sigma) \, pdf$')
plt.scatter(Diameter,np.zeros(n),color="red", s = 10,label = 'Data Set')
plt.axvline(mu_0, lw=1, ls = '--',color = 'blue',alpha=0.5)
plt.axvline(x_bar, lw=1, ls = '--',color = 'red',alpha=0.5)

text_str = '$\mu_0 = $' + f'{mu_0:2.0f}'
plt.text(mu_0,11,text_str,horizontalalignment='right',color = 'blue')

text_str = r'$\overline{x} = $' + f'{x_bar:2.2f}'
plt.text(x_bar+0.005,11,text_str,horizontalalignment='left',color = 'red')

text_str = r'$H_0: \mu = \mu_0$'
plt.text(LB-off_set_x+0.005,11,text_str,horizontalalignment='left',color = 'red')

text_str = r'$H_1: \mu \neq \mu_0$'
plt.text(LB-off_set_x+0.005,10.25,text_str,horizontalalignment='left',color = 'red')

text_str = r'$s_n = $' + f'{s_n:2.3f}'
plt.text(LB-off_set_x+0.005,9.5,text_str,horizontalalignment='left',color = 'red')

text_str = "Ball Bearing Example $X \sim N(\mu,\sigma), \mu = \mu_0 = $" + f'{mu_0:2.0f}' + ', $\sigma = s_n$, $n = $' + str(n)
Figure.suptitle(text_str,size='14')

plt.legend(loc = 'best')

plt.savefig('Bearing_example_1.png', dpi=300)