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

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 [R134].

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 [R132], or the time between page requests to Wikipedia [R133].


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.


[R132](1, 2) Peyton Z. Peebles Jr., “Probability, Random Variables and Random Signal Principles”, 4th ed, 2001, p. 57.
[R133](1, 2) “Poisson Process”, Wikipedia,
[R134](1, 2) “Exponential Distribution, Wikipedia,