xorbits.numpy.random.exponential#

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.

Note

New code should use the ~numpy.random.Generator.exponential method of a ~numpy.random.Generator instance instead; please see the random-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 – Drawn samples from the parameterized exponential distribution.

Return type

ndarray or scalar

Examples

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