xorbits.numpy.random.exponential(scale=1.0, size=None)[source]#

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.


New code should use the ~numpy.random.Generator.exponential method of a ~numpy.random.Generator instance instead; please see the random-quick-start.

  • 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.


out – Drawn samples from the parameterized exponential distribution.

Return type

ndarray or scalar


A real world example: Assume a company has 10000 customer support agents and the average time between customer calls is 4 minutes.

>>> n = 10000  
>>> time_between_calls = np.random.default_rng().exponential(scale=4, size=n)  

What is the probability that a customer will call in the next 4 to 5 minutes?

>>> x = ((time_between_calls < 5).sum())/n   
>>> y = ((time_between_calls < 4).sum())/n  
>>> x-y  
0.08 # may vary

See also


which should be used for new code.



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


Wikipedia, “Poisson process”, https://en.wikipedia.org/wiki/Poisson_process


Wikipedia, “Exponential distribution”, https://en.wikipedia.org/wiki/Exponential_distribution

This docstring was copied from numpy.random.