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bundles / numpy 2.4.3 / numpy / random / RandomState / laplace

cython_function_or_method

numpy.random:RandomState.laplace

Signature

def   laplace ( loc = 0.0 ,  scale = 1.0 ,  size = None )

Summary

Draw samples from the Laplace or double exponential distribution with specified location (or mean) and scale (decay).

Extended Summary

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.

Parameters

loc : float or array_like of floats, optional

The position, , of the distribution peak. Default is 0.

scale : float or array_like of floats, optional

, the exponential decay. Default is 1. Must be non- negative.

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.

Returns

out : ndarray or scalar

Drawn samples from the parameterized Laplace distribution.

Notes

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.

Examples

Draw samples from the distribution 
loc, scale = 0., 1.
s = np.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, 30, density=True)
x = np.arange(-8., 8., .01)
pdf = np.exp(-abs(x-loc)/scale)/(2.*scale)
✓
plt.plot(x, pdf)
✗
Plot Gaussian for comparison: 
g = (1/(scale * np.sqrt(2 * np.pi)) *
     np.exp(-(x - loc)**2 / (2 * scale**2)))
✓
plt.plot(x,g)
✗

See also

random.Generator.laplace

which should be used for new code.

Aliases

  • numpy.random.laplace
  • numpy.random.RandomState.laplace