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Module « numpy.random »
Signature de la fonction exponential
def exponential(scale=1.0, size=None)
Description
help(numpy.random.exponential)
exponential(scale=1.0, size=None)
Draw samples from an exponential distribution.
Its probability density function is
.. math:: f(x; \frac{1}{\beta}) = \frac{1}{\beta} \exp(-\frac{x}{\beta}),
for ``x > 0`` and 0 elsewhere. :math:`\beta` is the scale parameter,
which is the inverse of the rate parameter :math:`\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 :ref:`random-quick-start`.
Parameters
----------
scale : float or array_like of floats
The scale parameter, :math:`\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.
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
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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