flopscope.numpy.random.Generator.exponential

fnp.random.Generator.exponential(self, scale=1.0, size=None)

Draw samples from an exponential distribution.

Adapted from NumPy docs np.random.Generator.exponential

Arearandom

Typecounted

NumPy Refnp.random.Generator.exponential

Cost

\text{numel}(\text{output})

Flopscope Context

Exponential distribution; cost = numel(output).

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, $\beta = 1/\lambda$ . 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, flops.array(scale).size samples are drawn.

Returns

out:ndarray or scalar: Drawn samples from the parameterized exponential distribution.

References

footnote

1

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

footnote

2

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

footnote

3

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

Examples

Assume a company has 10000 customer support agents and the time between customer calls is exponentially distributed and that the average time between customer calls is 4 minutes.

>>> scale, size = 4, 10000
>>> rng = flops.random.default_rng()
>>> time_between_calls = rng.exponential(scale=scale, size=size)

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

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

The corresponding distribution can be visualized as follows:

>>> import matplotlib.pyplot as plt
>>> scale, size = 4, 10000
>>> rng = flops.random.default_rng()
>>> sample = rng.exponential(scale=scale, size=size)
>>> count, bins, _ = plt.hist(sample, 30, density=True)
>>> plt.plot(bins, scale**(-1)*flops.exp(-scale**-1*bins), linewidth=2, color='r')
>>> plt.show()