normal(self, loc=0.0, scale=1.0, size=None, chunks='auto', **kwargs)
This docstring was copied from numpy.random.mtrand.RandomState.normal.
Some inconsistencies with the Dask version may exist.
The probability density function of the normal distribution, first derived by De Moivre and 200 years later by both Gauss and Laplace independently , 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 .
New code should use the normal
method of a default_rng()
instance instead; please see the :None:ref:`random-quick-start`.
The probability density for the Gaussian distribution is
$$p(x) = \frac{1}{\sqrt{ 2 \pi \sigma^2 }}e^{ - \frac{ (x - \mu)^2 } {2 \sigma^2} },$$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 $x - \sigma$ ). This implies that normal is more likely to return samples lying close to the mean, rather than those far away.
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.
Drawn samples from the parameterized normal distribution.
Draw random samples from a normal (Gaussian) distribution.
Generator.normal
which should be used for new code.
scipy.stats.norm
probability density function, distribution or cumulative density function, etc.
Draw samples from the distribution:
This example is valid syntax, but we were not able to check execution>>> mu, sigma = 0, 0.1 # mean and standard deviation # doctest: +SKIP
... s = np.random.normal(mu, sigma, 1000) # doctest: +SKIP
Verify the mean and the variance:
This example is valid syntax, but we were not able to check execution>>> abs(mu - np.mean(s)) # doctest: +SKIP 0.0 # may varyThis example is valid syntax, but we were not able to check execution
>>> abs(sigma - np.std(s, ddof=1)) # doctest: +SKIP 0.1 # may vary
Display the histogram of the samples, along with the probability density function:
This example is valid syntax, but we were not able to check execution>>> import matplotlib.pyplot as plt # doctest: +SKIP
... count, bins, ignored = plt.hist(s, 30, density=True) # doctest: +SKIP
... plt.plot(bins, 1/(sigma * np.sqrt(2 * np.pi)) * # doctest: +SKIP
... np.exp( - (bins - mu)**2 / (2 * sigma**2) ),
... linewidth=2, color='r')
... plt.show() # doctest: +SKIP
Two-by-four array of samples from N(3, 6.25):
This example is valid syntax, but we were not able to check execution>>> np.random.normal(3, 2.5, size=(2, 4)) # doctest: +SKIP array([[-4.49401501, 4.00950034, -1.81814867, 7.29718677], # random [ 0.39924804, 4.68456316, 4.99394529, 4.84057254]]) # randomSee :
The following pages refer to to this document either explicitly or contain code examples using this.
dask.array.gufunc.apply_gufunc
dask.array.random.RandomState
dask.array.gufunc.as_gufunc
dask.array.gufunc.gufunc
dask.array.random.RandomState.standard_normal
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