Generating random numbers from a standard normal distribution

Normal distributions play a central role in finance. A major reason is that many finance theories, such as option theory and their related applications, are based on the assumption that stock returns follow a normal distribution. The second reason is that if our econometric models are well designed, the error terms from the models should follow a zero-mean normal distribution. It is a common task that we need to generate n random numbers from a standard normal distribution. For this purpose, we have the following three lines of code:

import scipy as sp
x=sp.random.standard_normal(size=10)
print(x)
[-0.98350472  0.93094376 -0.81167564 -1.83015626 -0.13873015  0.33408835
  0.48867499 -0.17809823  2.1223147   0.06119195]

The basic random numbers in SciPy/NumPy are created by Mersenne Twister PRNG in the numpy.random function. The random numbers for distributions in numpy.random are in cython/pyrex and are pretty fast. There is no...