In [54]:

    

import statistics
import scipy.stats as stats
import pandas as pd
import numpy as np
import ineqpy


    

In [42]:

    

x = np.random.randn(10)


    

In [43]:

    

w = abs(np.random.randn(10))
w = w / w.sum()


    

In [44]:

    

np.mean(x)


    

    
Out[44]:





0.079282307081652598

In [45]:

    

ineqpy.mean(variable=x)


    

    
Out[45]:





0.079282307081652598

In [46]:

    

np.var(x)


    

    
Out[46]:





0.26771028632127503

In [47]:

    

ineqpy.var(variable=x)


    

    
Out[47]:





0.26771028632127503

In [48]:

    

stats.skew(x)


    

    
Out[48]:





-0.08683494039388037

In [49]:

    

ineqpy.skew(variable=x)


    

    
Out[49]:





-0.086834940393880372

In [52]:

    

stats.kurtosis(x) + 3


    

    
Out[52]:





2.1915828922522693

In [51]:

    

ineqpy.kurt(variable=x)


    

    
Out[51]:





2.1915828922522693

In [4]:

    

x = np.array([1,2,2,3,3,3,4,4,4,4,5,5,5,5,5,6,6,6,6,7,7,7,8,8,9])


    

In [5]:

    

xi, fi = np.unique(x, return_counts=True)


    

In [6]:

    

xi # values


    

    
Out[6]:





array([1, 2, 3, 4, 5, 6, 7, 8, 9])

In [7]:

    

fi # absolute frequency


    

    
Out[7]:





array([1, 2, 3, 4, 5, 4, 3, 2, 1])

In [18]:

    

data = pd.DataFrame(np.c_[x, np.ones(len(x))], columns=list('xf'))


    

In [19]:

    

data


    

    
Out[19]:






  

    

      

      
x
      
f
    
  
  

    

      
0
      
1.0
      
1.0
    
    

      
1
      
2.0
      
1.0
    
    

      
2
      
2.0
      
1.0
    
    

      
3
      
3.0
      
1.0
    
    

      
4
      
3.0
      
1.0
    
    

      
5
      
3.0
      
1.0
    
    

      
6
      
4.0
      
1.0
    
    

      
7
      
4.0
      
1.0
    
    

      
8
      
4.0
      
1.0
    
    

      
9
      
4.0
      
1.0
    
    

      
10
      
5.0
      
1.0
    
    

      
11
      
5.0
      
1.0
    
    

      
12
      
5.0
      
1.0
    
    

      
13
      
5.0
      
1.0
    
    

      
14
      
5.0
      
1.0
    
    

      
15
      
6.0
      
1.0
    
    

      
16
      
6.0
      
1.0
    
    

      
17
      
6.0
      
1.0
    
    

      
18
      
6.0
      
1.0
    
    

      
19
      
7.0
      
1.0
    
    

      
20
      
7.0
      
1.0
    
    

      
21
      
7.0
      
1.0
    
    

      
22
      
8.0
      
1.0
    
    

      
23
      
8.0
      
1.0
    
    

      
24
      
9.0
      
1.0
    
  

In [20]:

    

data_weighted = pd.DataFrame(np.c_[xi,fi], columns=list('xf'))


    

In [21]:

    

data_weighted


    

    
Out[21]:






  

    

      

      
x
      
f
    
  
  

    

      
0
      
1
      
1
    
    

      
1
      
2
      
2
    
    

      
2
      
3
      
3
    
    

      
3
      
4
      
4
    
    

      
4
      
5
      
5
    
    

      
5
      
6
      
4
    
    

      
6
      
7
      
3
    
    

      
7
      
8
      
2
    
    

      
8
      
9
      
1
    
  

In [22]:

    

np.mean(x)


    

    
Out[22]:





5.0

In [23]:

    

data.mean()


    

    
Out[23]:





x    5.0
f    1.0
dtype: float64

In [24]:

    

ineqpy.mean(variable=x)


    

    
Out[24]:





5.0

In [25]:

    

ineqpy.mean(data, 'x')


    

    
Out[25]:





5.0

In [26]:

    

ineqpy.mean(variable=xi, weights=fi)


    

    
Out[26]:





5.0

In [27]:

    

ineqpy.mean(data, 'x', 'f')


    

    
Out[27]:





5.0

In [28]:

    

np.var(x, ddof=1)  # numpy (ddof=1)


    

    
Out[28]:





4.166666666666667

In [29]:

    

stats.variation(x)  # scipy (ddof=0)


    

    
Out[29]:





0.40000000000000002

In [30]:

    

data.var()  # pandas (ddof=1)


    

    
Out[30]:





x    4.166667
f    0.000000
dtype: float64

In [31]:

    

ineqpy.var(variable=x)


    

    
Out[31]:





4.0

In [32]:

    

ineqpy.var(variable=xi, weights=fi)


    

    
Out[32]:





4.0

In [33]:

    

stats.skew(x)


    

    
Out[33]:





0.0

In [41]:

    

data.skew()


    

    
Out[41]:





x    0.0
f    0.0
dtype: float64

In [34]:

    

ineqpy.skew(variable=x)


    

    
Out[34]:





0.0

In [35]:

    

ineqpy.skew(variable=xi, weights=fi)


    

    
Out[35]:





0.0

In [36]:

    

stats.kurtosis(x) + 3


    

    
Out[36]:





2.35

In [40]:

    

data.kurt()+3


    

    
Out[40]:





x    2.483004
f    3.000000
dtype: float64

In [37]:

    

ineqpy.kurt(variable=x)


    

    
Out[37]:





2.3500000000000001

In [38]:

    

ineqpy.kurt(variable=xi, weights=fi)


    

    
Out[38]:





2.3500000000000001

In [ ]: