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].
Parameters:Mean (âcentreâ) of the distribution.
Standard deviation (spread or âwidthâ) of the distribution.
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.
Drawn samples from the parameterized normal distribution.
See also
scipy.stats.norm
Notes
The probability density for the Gaussian distribution is
where is the mean and the standard deviation. The square of the standard deviation, , is called the variance.
The function has its peak at the mean, and its âspreadâ increases with the standard deviation (the function reaches 0.607 times its maximum at and [2]). This implies that numpy.random.normal
is more likely to return samples lying close to the mean, rather than those far away.
References
[2] (1, 2, 3, 4) P. R. Peebles Jr., âCentral Limit Theoremâ in âProbability, Random Variables and Random Signal Principlesâ, 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.normal(mu, sigma, 1000)
Verify the mean and the variance:
>>> abs(mu - np.mean(s)) < 0.01 True
>>> abs(sigma - np.std(s, ddof=1)) < 0.01 True
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()
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