NumPy Random Module

NumPy's random module is a powerful tool for generating random numbers, permutations, and various probability distributions. It's widely used in simulations, statistics, and machine learning to introduce randomness into computations.

Random Number Generation:

np.random.rand()

This function generates random numbers from a uniform distribution in the interval 0 to 1. This means that all values in the output array are equally likely, and there is no clustering around any particular value. The generated numbers are between 0 (inclusive) and 1 (exclusive). It's useful for generating random data that doesn't necessarily follow a specific distribution.

import numpy as np
 
# Generate random numbers from a uniform distribution [0, 1)
random_numbers = np.random.rand(3, 2)
print(random_numbers)

np.random.randint()

This function generates random integers within a specified range. You can specify the lower bound (inclusive) and upper bound (exclusive) of the range. The size parameter determines the shape of the output array.

# Generate random integers in the range [1, 10) with size 5
random_integers = np.random.randint(1, 10, size=5)
 
print(random_integers) # [2 3 4 8 6]

You can also generate 2D array

# 2D array of shape (2, 3) with random integers between 0 and 10
random_integers_2d = np.random.randint(low=0, high=10, size=(2, 3))
 
print(random_integers_2d)

np.random.randn()

This function generates random numbers from a standard normal distribution with mean 0 and standard deviation 1. The generated values are more likely to be around 0, with tails tapering off as they move away from 0.

# Generate random numbers from standard normal distribution (mean=0, std=1)
random_normal = np.random.randn(3, 2)
 
print(random_normal)

np.random.random()

This function is similar to np.random.rand(). It generates random numbers from a uniform distribution over the interval 0 to 1

# Generate a single random numbers from a uniform distribution [0, 1)
random_number = np.random.random()
 
print(random_numbers) # 0.9679494167233668

Permutations

np.random.shuffle()

The np.random.shuffle function is used to shuffle the elements of the array randomly. The shuffle function modifies the array in-place, rearranging its elements in a random order.

array = np.array([1, 2, 3, 4, 5])
np.random.shuffle(array)
 
print(array) # [3 2 4 1 5] 

np.random.permutation()

This function returns a shuffled copy of the input array. It doesn't modify the original array as np.random.shuffle() does

array = np.array([1, 2, 3, 4, 5])
shuffled_array = np.random.permutation(array)
 
print(shuffled_array) # [5 3 1 2 4]
print(array) # [1 2 3 4 5]

Distributions

np.random.uniform()

This function generates random numbers from a uniform distribution over a specified interval (low, high).

# Generating a uniform distribution
# Parameters: low = 0, high = 1
# Generating 5 random samples from the uniform distribution
uniform_distribution = np.random.uniform(0, 1, size=5)
 
# Printing the generated uniform distribution
print(uniform_distribution)

np.random.normal()

This function generates random numbers from a normal distribution with specified mean and standard deviation.

# Generating a normal distribution
# Parameters: mean = 10, standard deviation = 2
# Generating 5 random samples from the normal distribution
normal_distribution = np.random.normal(10, 2, size=5)
 
# Printing the generated normal distribution
print(normal_distribution)

np.random.binomial()

This function generates random numbers from a binomial distribution. It simulates the number of successes in a fixed number of independent Bernoulli trials.

# Generating a binomial distribution
# Parameters: n = 10 (number of trials), p = 0.5 (probability of success)
# Generating 5 random samples from the binomial distribution
binomial_distribution = np.random.binomial(10, 0.5, size=5)
 
# Printing the generated binomial distribution
print(binomial_distribution)

Summary of Distributions

Here is a table summarizing the main features of the uniform, normal, and binomial distributions and their corresponding functions in NumPy:

In the syntax:

• low and high specify the range of the uniform distribution.
• mean and std_dev specify the mean and standard deviation of the normal distribution.
• n and p specify the number of trials and the probability of success for the binomial distribution.
• size specifies the output shape for all three functions.