# numpy.random.RandomState.exponential

method

random.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 [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; please see the Quick Start.

  Parameters
    scale float or array_like of floats

      The scale parameter, \(\beta = 1/\lambda\). Must be non-negative.

    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.

  See also

  `random.Generator.exponential`

    which should be used for new code.

  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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