An important part of any simulation is the ability to generate random numbers. For this purpose, NumPy provides various routines in the submodule random. It uses a particular algorithm, called the Mersenne Twister, to generate pseudorandom numbers.

First, we need to define a seed that makes the random numbers predictable. When the value is reset, the same numbers will appear every time. If we do not assign the seed, NumPy automatically selects a random seed value based on the system's random number generator device or on the clock:

>>> np.random.seed(20)

An array of random numbers in the [0.0, 1.0] interval can be generated as follows:

>>> np.random.rand(5)
array([0.5881308, 0.89771373, 0.89153073, 0.81583748, 
         0.03588959])
>>> np.random.rand(5)
array([0.69175758, 0.37868094, 0.51851095, 0.65795147,  
       0.19385022])

>>> np.random.seed(20)    # reset seed number
>>> np.random.rand(5)
array([0.5881308, 0.89771373, 0.89153073, 0.81583748,  
       0.03588959])

If we want to generate random integers in the half-open interval [min, max], we can user the randint(min, max, length) function:

>>> np.random.randint(10, 20, 5)
array([17, 12, 10, 16, 18])

NumPy also provides for many other distributions, including the Beta, bionomial, chi-square, Dirichlet, exponential, F, Gamma, geometric, or Gumbel.

The following table will list some distribution functions and give examples for generating random numbers:

>>> n, p = 100, 0.2
>>> np.random.binomial(n, p, 3)
array([17, 14, 23])

>>> np.random.dirichlet(alpha=(2,3), size=3)
array([[0.519, 0.480], [0.639, 0.36],
 [0.838, 0.161]])

>>> np.random.poisson(lam=2, size= 2)
array([4,1])

>>> np.random.normal
(loc=2.5, scale=0.3, size=3)
array([2.4436, 2.849, 2.741)

>>> np.random.uniform(
low=0.5, high=2.5, size=3)
array([1.38, 1.04, 2.19[)

We can also use the random number generation to shuffle items in a list. Sometimes this is useful when we want to sort a list in a random order:

>>> a = np.arange(10)
>>> np.random.shuffle(a)
>>> a
array([7, 6, 3, 1, 4, 2, 5, 0, 9, 8])

The following figure shows two distributions, binomial and poisson , side by side with various parameters (the visualization was created with matplotlib, which will be covered in Chapter 4, Data Visualization):