`numpy.random._generator:Generator.normal`

Signature

def normal ( loc = 0.0 , scale = 1.0 , size = None )

Summary

Draw random samples from a normal (Gaussian) distribution.

Extended Summary

The probability density function of the normal distribution, first derived by De Moivre and 200 years later by both Gauss and Laplace independently ^[2], is often called the bell curve because of its characteristic shape (see the example below).

The normal distributions occurs often in nature. For example, it describes the commonly occurring distribution of samples influenced by a large number of tiny, random disturbances, each with its own unique distribution ^[2].

Parameters

loc : float or array_like of floats: Mean ("centre") of the distribution.
scale : float or array_like of floats: Standard deviation (spread or "width") of the distribution. Must be non-negative.
size : int or tuple of ints, optional: Output shape. If the given shape is, e.g., (m, n, k), then m * n * k samples are drawn. If size is None (default), a single value is returned if loc and scale are both scalars. Otherwise, np.broadcast(loc, scale).size samples are drawn.

Returns

out : ndarray or scalar: Drawn samples from the parameterized normal distribution.

Notes

The probability density for the Gaussian distribution is

p (x) = \frac{1}{2 π σ ^{2}} e^{- \frac{( x - μ ) ^{2}}{2 σ ^{2}}},

where $μ$ is the mean and $σ$ the standard deviation. The square of the standard deviation, $σ^{2}$ , is called the variance.

The function has its peak at the mean, and its "spread" increases with the standard deviation (the function reaches 0.607 times its maximum at $x + σ$ and $x - σ$ ^[2]). This implies that normal is more likely to return samples lying close to the mean, rather than those far away.

Examples

Draw samples from the distribution:

mu, sigma = 0, 0.1 # mean and standard deviation
rng = np.random.default_rng()
s = rng.normal(mu, sigma, 1000)

✓

Verify the mean and the standard deviation:

abs(mu - np.mean(s))

✗

abs(sigma - np.std(s, ddof=1))

✗

Display the histogram of the samples, along with the probability density function:

import matplotlib.pyplot as plt
count, bins, _ = plt.hist(s, 30, density=True)

✓

plt.plot(bins, 1/(sigma * np.sqrt(2 * np.pi)) *
               np.exp( - (bins - mu)**2 / (2 * sigma**2) ),
         linewidth=2, color='r')

✗

plt.show()

✓

Two-by-four array of samples from the normal distribution with mean 3 and standard deviation 2.5:

rng = np.random.default_rng()

✓

rng.normal(3, 2.5, size=(2, 4))

`numpy.random._generator:Generator.normal`

Signature

Summary

Extended Summary

Parameters

Returns

Notes

Examples

See also

Aliases

Referenced by

This package