flopscope.

flopscope.numpy.random.RandomState.exponential

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

Draw samples from an exponential distribution.

Adapted from NumPy docs np.random.RandomState.exponential

Arearandom
Typecounted
NumPy Refnp.random.RandomState.exponential
Cost
numel(output)\text{numel}(\text{output})
Flopscope Context

Legacy exponential sampler; cost = numel(output).

Its probability density function is

f(x;1β)=1βexp⁡(−xβ),f(x; \frac{1}{\beta}) = \frac{1}{\beta} \exp(-\frac{x}{\beta}),

for x > 0 and 0 elsewhere. β\beta is the scale parameter, which is the inverse of the rate parameter λ=1/β\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 Generator instance instead; please see the random-quick-start.

Parameters

scale:float or array_like of floats

The scale parameter, β=1/λ\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.

See also

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

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 = flops.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