numpy.random.RandomState.exponential

RandomState.exponential(scale=1.0, size=None)

Draw samples from an exponential distribution.

Its probability density function is

$f(x; \frac{1}{\beta}) = \frac{1}{\beta} \exp(-\frac{x}{\beta}),$

for x > 0 and 0 elsewhere. $\beta$ is the scale parameter, which is the inverse of the rate parameter $\lambda = 1/\beta$ . The rate parameter is an alternative, widely used parameterization of the exponential distribution [3].

The exponential distribution is a continuous analogue of the geometric distribution. It describes many common situations, such as the size of raindrops measured over many rainstorms [1], or the time between page requests to Wikipedia [2].

Parameters:	`scale : float or array_like of floats` The scale parameter, $\beta = 1/\lambda$ . `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 `scale` is a scalar. Otherwise, `np.array(scale).size` samples are drawn.
Returns:	`out : ndarray or scalar` Drawn samples from the parameterized exponential distribution.

References

[1]	(1, 2) Peyton Z. Peebles Jr., “Probability, Random Variables and Random Signal Principles”, 4th ed, 2001, p. 57.

[2]	(1, 2) Wikipedia, “Poisson process”, http://en.wikipedia.org/wiki/Poisson_process

[3]	(1, 2) Wikipedia, “Exponential distribution”, http://en.wikipedia.org/wiki/Exponential_distribution

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