Time for action – sampling with numpy.random.choice()

We will use the numpy.random.choice() function to perform bootstrapping.

1. Start the IPython or Python shell and import NumPy:

   $ ipython
   In [1]: import numpy as np
   

2. Generate a data sample following the normal distribution:

   In [2]: N = 500
   
   In [3]: np.random.seed(52)
   
   In [4]: data = np.random.normal(size=N)
   

3. Calculate the mean of the data:

   In [5]: data.mean()
   Out[5]: 0.07253250605445645
   

   Generate 100 samples from the original data and calculate their means (of course, more samples may lead to a more accurate result):

   In [6]: bootstrapped = np.random.choice(data, size=(N, 100))
   
   In [7]: means = bootstrapped.mean(axis=0)
   
   In [8]: means.shape
   Out[8]: (100,)
   

4. Calculate the mean, variance, and standard deviation of the arithmetic means we obtained:

   In [9]: means.mean()
   Out[9]: 0.067866373318115278
   
   In [10]: means.var()
   Out[10]: 0.001762807104774598
   
   In [11]: means.std()
   Out[11]: 0.041985796464692651
   

   If we are assuming a normal distribution for...