# -*- coding: utf-8 -*-
"""
Created on Fri Jun  4 10:44:37 2021

@author: Sim
"""
import numpy as np
import pandas as pd
from scipy.stats import skew
from scipy.stats import kurtosis
import matplotlib.pyplot as plt

np.random.seed(1000)
x = pd.Series(np.random.normal(0,1,1000))
x.hist()
plt.show()
sk1 = x.skew()
sk2 = skew(x)
kt1 = x.kurtosis()
kt2 = kurtosis(x)

print(sk1, sk2, kt1, kt2)

y = pd.Series(np.random.chisquare(4,1000))
y.hist()
plt.show()
sk3 = y.skew()
sk4 = skew(y)
kt3 = y.kurtosis()
kt4 = kurtosis(y)
print(sk3, sk4, kt3, kt4)

num1 = np.sum( (x - np.mean(x))**3 )/1000 
denom1 = ( np.sum( (x - np.mean(x))**2 ) /1000 ) **1.5
skew1 = num1/denom1

skew2 = (1000**2)/(999*998) *skew1

print(skew1, skew2)