4.2.1.1.7. 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 [R83].

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 [R81], or the time between page requests to Wikipedia [R82].

Parameters:

scale : float

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. Default is None, in which case a single value is returned.

References

[R81]

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

[R82]

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

[R83]

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