numpy.random.exponential

numpy.random.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].

Note

New code should use the exponential method of a default_rng() instance instead; see random-quick-start.

Parameters

scalefloat or array_like of floats: The scale parameter, $\beta = 1/\lambda$ . Must be non-negative.
sizeint 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

outndarray or scalar: Drawn samples from the parameterized exponential distribution.

References

1: Peyton Z. Peebles Jr., “Probability, Random Variables and Random Signal Principles”, 4th ed, 2001, p. 57.
2: Wikipedia, “Poisson process”, https://en.wikipedia.org/wiki/Poisson_process
3: Wikipedia, “Exponential distribution”, https://en.wikipedia.org/wiki/Exponential_distribution

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https://numpy.org/doc/1.19/reference/random/generated/numpy.random.exponential.html