Python Pandas - Statistical Functions

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Statistical methods help in the understanding and analyzing the behavior of data. We will now learn a few statistical functions, which we can apply on Pandas objects.

Percent_change

Series, DatFrames and Panel, all have the function pct_change(). This function compares every element with its prior element and computes the change percentage.

Live Demo 
import pandas as pd
import numpy as np
s = pd.Series([1,2,3,4,5,4])
print s.pct_change()

df = pd.DataFrame(np.random.randn(5, 2))
print df.pct_change()

Its output is as follows −

0        NaN
1   1.000000
2   0.500000
3   0.333333
4   0.250000
5  -0.200000
dtype: float64

            0          1
0         NaN        NaN
1  -15.151902   0.174730
2  -0.746374   -1.449088
3  -3.582229   -3.165836
4   15.601150  -1.860434

By default, the pct_change() operates on columns; if you want to apply the same row wise, then use axis=1() argument.

Covariance

Covariance is applied on series data. The Series object has a method cov to compute covariance between series objects. NA will be excluded automatically.

Cov Series

Live Demo 
import pandas as pd
import numpy as np
s1 = pd.Series(np.random.randn(10))
s2 = pd.Series(np.random.randn(10))
print s1.cov(s2)

Its output is as follows −

-0.12978405324

Covariance method when applied on a DataFrame, computes cov between all the columns.

Live Demo 
import pandas as pd
import numpy as np
frame = pd.DataFrame(np.random.randn(10, 5), columns=['a', 'b', 'c', 'd', 'e'])
print frame['a'].cov(frame['b'])
print frame.cov()

Its output is as follows −

-0.58312921152741437

           a           b           c           d            e
a   1.780628   -0.583129   -0.185575    0.003679    -0.136558
b  -0.583129    1.297011    0.136530   -0.523719     0.251064
c  -0.185575    0.136530    0.915227   -0.053881    -0.058926
d   0.003679   -0.523719   -0.053881    1.521426    -0.487694
e  -0.136558    0.251064   -0.058926   -0.487694     0.960761

Note − Observe the cov between a and b column in the first statement and the same is the value returned by cov on DataFrame.

Correlation

Correlation shows the linear relationship between any two array of values (series). There are multiple methods to compute the correlation like pearson(default), spearman and kendall.

Live Demo 
import pandas as pd
import numpy as np
frame = pd.DataFrame(np.random.randn(10, 5), columns=['a', 'b', 'c', 'd', 'e'])

print frame['a'].corr(frame['b'])
print frame.corr()

Its output is as follows −

-0.383712785514

           a          b          c          d           e
a   1.000000  -0.383713  -0.145368   0.002235   -0.104405
b  -0.383713   1.000000   0.125311  -0.372821    0.224908
c  -0.145368   0.125311   1.000000  -0.045661   -0.062840
d   0.002235  -0.372821  -0.045661   1.000000   -0.403380
e  -0.104405   0.224908  -0.062840  -0.403380    1.000000

If any non-numeric column is present in the DataFrame, it is excluded automatically.

Data Ranking

Data Ranking produces ranking for each element in the array of elements. In case of ties, assigns the mean rank.

Live Demo 
import pandas as pd
import numpy as np

s = pd.Series(np.random.np.random.randn(5), index=list('abcde'))
s['d'] = s['b'] # so there's a tie
print s.rank()

Its output is as follows −

a  1.0
b  3.5
c  2.0
d  3.5
e  5.0
dtype: float64

Rank optionally takes a parameter ascending which by default is true; when false, data is reverse-ranked, with larger values assigned a smaller rank.

Rank supports different tie-breaking methods, specified with the method parameter −

  • average − average rank of tied group

  • min − lowest rank in the group

  • max − highest rank in the group

  • first − ranks assigned in the order they appear in the array

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