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 [R152].

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 [R150], or the time between page requests to Wikipedia [R151].

Parameters:

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.

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

[R150]

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

[R151]

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

[R152]

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