Understanding the Difference Between np.random.rand() and np.random.randn() in NumPy

When working with NumPy in Python, generating random numbers is a common task. Two functions that often cause confusion are

np.random.rand()
np.random.randn()

They look almost the same, but they generate numbers from different distributions. Let’s explore the difference with examples and outputs.

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1. np.random.rand() → Uniform Distribution

• Generates numbers between 0 and 1.

• Follows a uniform distribution → every number in the range [0, 1) has the same probability.

• Values are always non-negative.

Example:

import numpy as np

# 5 random numbers between 0 and 1
print(np.random.rand(5))

Sample Output:

[0.3745 0.9507 0.7319 0.5986 0.1560]

Visualization

import matplotlib.pyplot as plt

plt.subplot(1, 2, 1)
plt.hist(data_uniform, bins=30, color="skyblue", edgecolor="black")
plt.title("Uniform Distribution (np.random.rand)")
plt.xlabel("Value")
plt.ylabel("Frequency")

Output Plot:

(Flat distribution, values evenly spread in [0,1))

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2. np.random.randn() → Standard Normal Distribution

• Generates numbers from a standard normal distribution (Gaussian).

• Mean = 0, Standard Deviation = 1.

• Values can be negative or positive, but most cluster around 0.

Example

# 5 random numbers from standard normal distribution
print(np.random.randn(5))

Sample Output:

[-0.479  0.930 -0.185 -1.063  0.323]

Visualization

plt.subplot(1, 2, 2)
plt.hist(data_normal, bins=30, color="lightcoral", edgecolor="black")
plt.title("Normal Distribution (np.random.randn)")
plt.xlabel("Value")
plt.ylabel("Frequency")

Output Plot:

(Bell-shaped curve centered around 0)

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3. Side-by-Side Comparison

plt.figure(figsize=(12, 5))

# Uniform
plt.subplot(1, 2, 1)
plt.hist(data_uniform, bins=30, color="skyblue", edgecolor="black")
plt.title("Uniform Distribution (np.random.rand)")
plt.xlabel("Value")
plt.ylabel("Frequency")

# Normal
plt.subplot(1, 2, 2)
plt.hist(data_normal, bins=30, color="lightcoral", edgecolor="black")
plt.title("Normal Distribution (np.random.randn)")
plt.xlabel("Value")
plt.ylabel("Frequency")

plt.tight_layout()
plt.show()

Output Plot (Comparison):

• Left (rand) → flat distribution in [0,1).

• Right (randn) → bell curve centered at 0.

  

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4. Quick Summary

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Key Takeaway

• np.random.rand() → Flat uniform randomness between 0 and 1.

• np.random.randn() → Gaussian randomness centered at 0.

The difference is crucial in statistics, simulations and machine learning, where the choice of distribution directly impacts results.