laplace(self, loc=0.0, scale=1.0, size=None, chunks='auto', **kwargs)
This docstring was copied from numpy.random.mtrand.RandomState.laplace.
Some inconsistencies with the Dask version may exist.
The Laplace distribution is similar to the Gaussian/normal distribution, but is sharper at the peak and has fatter tails. It represents the difference between two independent, identically distributed exponential random variables.
New code should use the laplace
method of a default_rng()
instance instead; please see the :None:ref:`random-quick-start`.
It has the probability density function
$$f(x; \mu, \lambda) = \frac{1}{2\lambda}\exp\left(-\frac{|x - \mu|}{\lambda}\right).$$The first law of Laplace, from 1774, states that the frequency of an error can be expressed as an exponential function of the absolute magnitude of the error, which leads to the Laplace distribution. For many problems in economics and health sciences, this distribution seems to model the data better than the standard Gaussian distribution.
The position, $\mu$ , of the distribution peak. Default is 0.
$\lambda$ , the exponential decay. Default is 1. 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 Laplace distribution.
Draw samples from the Laplace or double exponential distribution with specified location (or mean) and scale (decay).
Generator.laplace
which should be used for new code.
Draw samples from the distribution
This example is valid syntax, but we were not able to check execution>>> loc, scale = 0., 1. # doctest: +SKIP
... s = np.random.laplace(loc, scale, 1000) # doctest: +SKIP
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
... x = np.arange(-8., 8., .01) # doctest: +SKIP
... pdf = np.exp(-abs(x-loc)/scale)/(2.*scale) # doctest: +SKIP
... plt.plot(x, pdf) # doctest: +SKIP
Plot Gaussian for comparison:
This example is valid syntax, but we were not able to check execution>>> g = (1/(scale * np.sqrt(2 * np.pi)) * # doctest: +SKIPSee :
... np.exp(-(x - loc)**2 / (2 * scale**2)))
... plt.plot(x,g) # doctest: +SKIP
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