normal

normal(loc=0.0, scale=1.0, size=None, dtype=None, ctx=None, out=None)

Draw random samples from a normal (Gaussian) distribution.

Samples are distributed according to a normal distribution parametrized by loc (mean) and scale (standard deviation).

Parameters:

loc : float, optional

Mean (centre) of the distribution.

scale : float, optional

Standard deviation (spread or “width”) of the distribution.

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 scalar tensor containing a single value is returned if loc and scale are both scalars. Otherwise, np.broadcast(low, high).size samples are drawn.

dtype : {‘float16’, ‘float32’, ‘float64’}, optional

Data type of output samples. Default is ‘float32’

ctx : Context, optional

Device context of output, default is current context.

out : ndarray, optional

Store output to an existing ndarray.

Returns:

out : ndarray

Drawn samples from the parameterized normal distribution.

Notes

The probability density for the Gaussian distribution is

(3)\[p(x) = \frac{1}{\sqrt{ 2 \pi \sigma^2 }} e^{ - \frac{ (x - \mu)^2 } {2 \sigma^2} },\]

where \(\mu\) is the mean and \(\sigma\) the standard deviation. The square of the standard deviation, \(\sigma^2\), 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 \(x + \sigma\) and \(x - \sigma\) [2]). This implies that numpy.random.normal is more likely to return samples lying close to the mean, rather than those far away.

References

[1]	Wikipedia, “Normal distribution”, https://en.wikipedia.org/wiki/Normal_distribution

[2]	P. R. Peebles Jr., “Central Limit Theorem” in “Probability, Random Variables and Random Signal Principles”, 4th ed., 2001, pp. 51, 51, 125.

Examples

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

Verify the mean and the variance:

>>> np.abs(mu - np.mean(s)) < 0.01
array(True)