Python:NumPy .normal()

The .normal() function from NumPy’s random module generates random numbers from a normal (Gaussian) distribution, which is a continuous, bell-shaped distribution commonly used in statistics and data science.

Syntax

numpy.random.normal(loc=0.0, scale=1.0, size=None)

Parameters:

• loc (float or array_like of floats, optional): The mean ($\mu$) of the distribution. Default is 0.0.
• scale (float or array_like of floats, optional): The standard deviation ($\sigma$) of the distribution. Must be non-negative. Default is 1.0.
• size (int or tuple of ints, optional): The output shape. Specifies the number or shape of random samples to generate. If None (default), a single sample is returned.

Return value:

• out (ndarray or scalar): Random samples from the normal distribution.
  • If size is None, returns a single float.
  • If size is specified, returns a NumPy array of the given shape with samples drawn from the normal distribution.

Statistical Properties

• Mean ($μ$) = loc
• Variance ($σ^2$) = $\text{scale}^2$

The Probability Density Function (PDF) of the normal distribution is:

$$ p(x) = \frac{1}{\sqrt{2\pi\sigma^2}} \ e^{-\frac{(x-\mu)^2}{2\sigma^2}} $$

• $\mu$ is the mean (loc).
• $\sigma$ is the standard deviation (scale).

Example

This example generates two reproducible random samples from a normal distribution with loc = 0 (mean) and scale = 1 (standard deviation):

import numpy as np
np.random.seed(15)
result = np.random.normal(loc=0, scale=1, size=2)
print(result)

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The output for this code will be:

[-0.44493578  0.22274619]

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Here:

• np.random.seed(15) ensures the same random numbers are generated every time the code runs.
• np.random.normal() draws two samples from the standard normal distribution.

Codebyte Example

This codebyte example generates a 2×3 array of normally distributed random numbers with loc = 5 (mean) and scale = 2 (standard deviation):

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• np.random.seed(42) sets the random seed for consistent results.
• size=(2, 3) creates a 2D array with 2 rows and 3 columns of normally distributed samples.