method
Generator.
normal
Draw random samples from a normal (Gaussian) distribution.
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].
Mean (“centre”) of the distribution.
Standard deviation (spread or “width”) of the distribution. Must be non-negative.
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.
(m, n, k)
m * n * k
None
loc
scale
np.broadcast(loc, scale).size
Drawn samples from the parameterized normal distribution.
See also
scipy.stats.norm
probability density function, distribution or cumulative density function, etc.
Notes
The probability density for the Gaussian distribution is
System Message: WARNING/2 (p(x) = \frac{1}{\sqrt{ 2 \pi \sigma^2 }} e^{ - \frac{ (x - \mu)^2 } {2 \sigma^2} }, )
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where
System Message: WARNING/2 (\mu)
System Message: WARNING/2 (\sigma)
System Message: WARNING/2 (\sigma^2)
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
System Message: WARNING/2 (x + \sigma)
System Message: WARNING/2 (x - \sigma)
References
Wikipedia, “Normal distribution”, https://en.wikipedia.org/wiki/Normal_distribution
P. R. Peebles Jr., “Central Limit Theorem” in “Probability, Random Variables and Random Signal Principles”, 4th ed., 2001, pp. 51, 51, 125.
Examples
Draw samples from the distribution:
>>> mu, sigma = 0, 0.1 # mean and standard deviation >>> s = np.random.default_rng().normal(mu, sigma, 1000)
Verify the mean and the variance:
>>> abs(mu - np.mean(s)) 0.0 # may vary
>>> abs(sigma - np.std(s, ddof=1)) 0.1 # may vary
Display the histogram of the samples, along with the probability density function:
>>> import matplotlib.pyplot as plt >>> count, bins, ignored = 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 N(3, 6.25):
>>> np.random.default_rng().normal(3, 2.5, size=(2, 4)) array([[-4.49401501, 4.00950034, -1.81814867, 7.29718677], # random [ 0.39924804, 4.68456316, 4.99394529, 4.84057254]]) # random