randomstate.prng.dsfmt.exponential

randomstate.prng.dsfmt.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 – Drawn samples from the parameterized exponential distribution.

Return type:

ndarray or scalar

References

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

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

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