Question

There are two modules for (pseudo) random numbers that are commonly used. When all you need is to generate random numbers from some distribtuion, the numpy.random moodule is the simplest to use. When you need more information realted to a disttribution such as quantiles or the PDF, you can use the scipy.stats module.

Module Reference

import numpy.random as npr
npr.seed(123) # fix seed for reproducible results

# 10 trials of rolling a fair 6-sided 100 times
roll = 1.0/6
x = npr.multinomial(100, [roll]*6, 10)
x

array([[18, 14, 14, 18, 20, 16],
       [16, 25, 16, 14, 14, 15],
       [15, 19, 16, 12, 18, 20],
       [19, 13, 14, 18, 18, 18],
       [18, 20, 17, 16, 16, 13],
       [15, 16, 15, 16, 20, 18],
       [12, 17, 17, 18, 17, 19],
       [15, 16, 22, 21, 13, 13],
       [18, 12, 16, 17, 22, 15],
       [14, 17, 25, 15, 15, 14]])

# uniformly distributed numbers in 2D
x = npr.uniform(-1, 1, (100, 2))
plt.scatter(x[:,0], x[:,1], s=50)
plt.axis([-1.05, 1.05, -1.05, 1.05]);

# ranodmly shuffling a vector
x = np.arange(10)
npr.shuffle(x)
x

array([5, 8, 6, 4, 3, 9, 1, 7, 2, 0])

# radnom permutations
npr.permutation(10)

array([1, 4, 9, 8, 6, 5, 3, 2, 0, 7])

# radnom selection without replacement
x = np.arange(10,20)
npr.choice(x, 10, replace=False)

array([14, 16, 15, 12, 19, 11, 13, 10, 18, 17])

# radnom selection with replacement
npr.choice(x, (5, 10), replace=True) # this is default

array([[15, 13, 10, 14, 18, 14, 19, 13, 15, 11],
       [18, 10, 19, 11, 15, 18, 18, 14, 16, 18],
       [17, 19, 12, 10, 10, 19, 19, 15, 13, 15],
       [15, 12, 12, 17, 13, 11, 13, 19, 13, 16],
       [12, 13, 11, 19, 18, 10, 12, 13, 17, 19]])

# toy example - estimating pi inefficiently
n = 1e6
x = npr.uniform(-1,1,(n,2))
4.0*np.sum(x[:,0]**2 + x[:,1]**2 < 1)/n

3.1416

Module refernce

import scipy.stats as stats

# Create a "frozen" distribution - i.e. a partially applied function
dist = stats.norm(10, 2)

#  same a rnorm
dist.rvs(10)

array([ 11.629 ,   9.5777,   8.5607,   8.5777,   8.6464,  11.5398,
        10.8751,  11.8244,  10.1772,   9.3056])

# same as pnorm
dist.pdf(np.linspace(5, 15, 10))

array([ 0.0088,  0.0301,  0.076 ,  0.141 ,  0.1919,  0.1919,  0.141 ,
        0.076 ,  0.0301,  0.0088])

# same as dnorm
dist.cdf(np.linspace(5, 15, 11))

array([ 0.0062,  0.0228,  0.0668,  0.1587,  0.3085,  0.5   ,  0.6915,
        0.8413,  0.9332,  0.9772,  0.9938])

# same as qnorm
dist.ppf(dist.cdf(np.linspace(5, 15, 11)))

array([  5.,   6.,   7.,   8.,   9.,  10.,  11.,  12.,  13.,  14.,  15.])