Statistics



In [1]:

    
__author__ = "kyubyong. kbpark.linguist@gmail.com"



In [2]:

    
import numpy as np



In [3]:

    
np.__version__









    Out[3]:





'1.11.3'

Order statistics

Q1. Return the minimum value of x along the second axis.



In [10]:

    
x = np.arange(4).reshape((2, 2))
print("x=\n", x)
print("ans=\n", np.amin(x, 1))









    



x=
 [[0 1]
 [2 3]]
ans=
 [0 2]

Q2. Return the maximum value of x along the second axis. Reduce the second axis to the dimension with size one.



In [12]:

    
x = np.arange(4).reshape((2, 2))
print("x=\n", x)
print("ans=\n", np.amax(x, 1, keepdims=True))









    



x=
 [[0 1]
 [2 3]]
ans=
 [[1]
 [3]]

Q3. Calcuate the difference between the maximum and the minimum of x along the second axis.



In [19]:

    
x = np.arange(10).reshape((2, 5))
print("x=\n", x)

out1 = np.ptp(x, 1)
out2 = np.amax(x, 1) - np.amin(x, 1)
assert np.allclose(out1, out2)
print("ans=\n", out1)









    



x=
 [[0 1 2 3 4]
 [5 6 7 8 9]]
ans=
 [4 4]

Q4. Compute the 75th percentile of x along the second axis.



In [30]:

    
x = np.arange(1, 11).reshape((2, 5))
print("x=\n", x)

print("ans=\n", np.percentile(x, 75, 1))









    



x=
 [[ 1  2  3  4  5]
 [ 6  7  8  9 10]]
ans=
 [ 4.  9.]

Averages and variances

Q5. Compute the median of flattened x.



In [33]:

    
x = np.arange(1, 10).reshape((3, 3))
print("x=\n", x)

print("ans=\n", np.median(x))









    



x=
 [[1 2 3]
 [4 5 6]
 [7 8 9]]
ans=
 5.0

Q6. Compute the weighted average of x.



In [62]:

    
x = np.arange(5)
weights = np.arange(1, 6)

out1 = np.average(x, weights=weights)
out2 = (x*(weights/weights.sum())).sum()
assert np.allclose(out1, out2)
print(out1)









    



2.66666666667

Q7. Compute the mean, standard deviation, and variance of x along the second axis.



In [72]:

    
x = np.arange(5)
print("x=\n",x)

out1 = np.mean(x)
out2 = np.average(x)
assert np.allclose(out1, out2)
print("mean=\n", out1)

out3 = np.std(x)
out4 = np.sqrt(np.mean((x - np.mean(x)) ** 2 ))
assert np.allclose(out3, out4)
print("std=\n", out3)

out5 = np.var(x)
out6 = np.mean((x - np.mean(x)) ** 2 )
assert np.allclose(out5, out6)
print("variance=\n", out5)









    



x=
 [0 1 2 3 4]
mean=
 2.0
std=
 1.41421356237
variance=
 2.0

Correlating

Q8. Compute the covariance matrix of x and y.



In [82]:

    
x = np.array([0, 1, 2])
y = np.array([2, 1, 0])

print("ans=\n", np.cov(x, y))









    



ans=
 [[ 1. -1.]
 [-1.  1.]]

Q9. In the above covariance matrix, what does the -1 mean?

It means x and y correlate perfectly in opposite directions.

Q10. Compute Pearson product-moment correlation coefficients of x and y.



In [87]:

    
x = np.array([0, 1, 3])
y = np.array([2, 4, 5])

print("ans=\n", np.corrcoef(x, y))









    



ans=
 [[ 1.          0.92857143]
 [ 0.92857143  1.        ]]

Q11. Compute cross-correlation of x and y.



In [90]:

    
x = np.array([0, 1, 3])
y = np.array([2, 4, 5])

print("ans=\n", np.correlate(x, y))









    



ans=
 [19]

Histograms

Q12. Compute the histogram of x against the bins.



In [105]:

    
x = np.array([0.5, 0.7, 1.0, 1.2, 1.3, 2.1])
bins = np.array([0, 1, 2, 3])
print("ans=\n", np.histogram(x, bins))

import matplotlib.pyplot as plt
%matplotlib inline
plt.hist(x, bins=bins)
plt.show()









    



ans=
 (array([2, 3, 1], dtype=int64), array([0, 1, 2, 3]))

Q13. Compute the 2d histogram of x and y.



In [127]:

    
xedges = [0, 1, 2, 3]
yedges = [0, 1, 2, 3, 4]
x = np.array([0, 0.1, 0.2, 1., 1.1, 2., 2.1])
y = np.array([0, 0.1, 0.2, 1., 1.1, 2., 3.3])
H, xedges, yedges = np.histogram2d(x, y, bins=(xedges, yedges))
print("ans=\n", H)

plt.scatter(x, y)
plt.grid()









    



ans=
 [[ 3.  0.  0.  0.]
 [ 0.  2.  0.  0.]
 [ 0.  0.  1.  1.]]

Q14. Count number of occurrences of 0 through 7 in x.



In [129]:

    
x = np.array([0, 1, 1, 3, 2, 1, 7])
print("ans=\n", np.bincount(x))









    



ans=
 [1 3 1 1 0 0 0 1]

Q15. Return the indices of the bins to which each value in x belongs.



In [130]:

    
x = np.array([0.2, 6.4, 3.0, 1.6])
bins = np.array([0.0, 1.0, 2.5, 4.0, 10.0])

print("ans=\n", np.digitize(x, bins))









    



ans=
 [1 4 3 2]



In [ ]: