Draw samples from the Laplace or double exponential distribution with
specified location (or mean) and scale (decay).
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
loc (float or array_like of floats, optional) – The position, \(\mu\), of the distribution peak. Default is 0.
scale (float or array_like of floats, optional) – \(\lambda\), the exponential decay. Default is 1.
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 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
chunks (int or tuple of int or tuple of ints, optional) – Desired chunk size on each dimension
gpu (bool, optional) – Allocate the tensor on GPU if True, False as default
dtype (data-type, optional) – Data-type of the returned tensor.
out – Drawn samples from the parameterized Laplace distribution.
Tensor or scalar
It has the probability density function
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.
Abramowitz, M. and Stegun, I. A. (Eds.). “Handbook of
Mathematical Functions with Formulas, Graphs, and Mathematical
Tables, 9th printing,” New York: Dover, 1972.
Kotz, Samuel, et. al. “The Laplace Distribution and
Generalizations, ” Birkhauser, 2001.
Weisstein, Eric W. “Laplace Distribution.”
From MathWorld–A Wolfram Web Resource.
Wikipedia, “Laplace distribution”,
Draw samples from the distribution
>>> import mars.tensor as mt
>>> loc, scale = 0., 1.
>>> s = mt.random.laplace(loc, scale, 1000)
Display the histogram of the samples, along with
the probability density function:
>>> import matplotlib.pyplot as plt
>>> count, bins, ignored = plt.hist(s.execute(), 30, normed=True)
>>> x = mt.arange(-8., 8., .01)
>>> pdf = mt.exp(-abs(x-loc)/scale)/(2.*scale)
>>> plt.plot(x.execute(), pdf.execute())
Plot Gaussian for comparison:
>>> g = (1/(scale * mt.sqrt(2 * np.pi)) *
... mt.exp(-(x - loc)**2 / (2 * scale**2)))