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Module « scipy.stats »

Fonction poisson - module scipy.stats

Signature de la fonction poisson

def poisson(*args, **kwds) 

Description

help(scipy.stats.poisson)

A Poisson discrete random variable.

As an instance of the `rv_discrete` class, `poisson` object inherits from it
a collection of generic methods (see below for the full list),
and completes them with details specific for this particular distribution.

Methods
-------
rvs(mu, loc=0, size=1, random_state=None)
    Random variates.
pmf(k, mu, loc=0)
    Probability mass function.
logpmf(k, mu, loc=0)
    Log of the probability mass function.
cdf(k, mu, loc=0)
    Cumulative distribution function.
logcdf(k, mu, loc=0)
    Log of the cumulative distribution function.
sf(k, mu, loc=0)
    Survival function  (also defined as ``1 - cdf``, but `sf` is sometimes more accurate).
logsf(k, mu, loc=0)
    Log of the survival function.
ppf(q, mu, loc=0)
    Percent point function (inverse of ``cdf`` --- percentiles).
isf(q, mu, loc=0)
    Inverse survival function (inverse of ``sf``).
stats(mu, loc=0, moments='mv')
    Mean('m'), variance('v'), skew('s'), and/or kurtosis('k').
entropy(mu, loc=0)
    (Differential) entropy of the RV.
expect(func, args=(mu,), loc=0, lb=None, ub=None, conditional=False)
    Expected value of a function (of one argument) with respect to the distribution.
median(mu, loc=0)
    Median of the distribution.
mean(mu, loc=0)
    Mean of the distribution.
var(mu, loc=0)
    Variance of the distribution.
std(mu, loc=0)
    Standard deviation of the distribution.
interval(confidence, mu, loc=0)
    Confidence interval with equal areas around the median.

Notes
-----
The probability mass function for `poisson` is:

.. math::

    f(k) = \exp(-\mu) \frac{\mu^k}{k!}

for :math:`k \ge 0`.

`poisson` takes :math:`\mu \geq 0` as shape parameter.
When :math:`\mu = 0`, the ``pmf`` method
returns ``1.0`` at quantile :math:`k = 0`.

The probability mass function above is defined in the "standardized" form.
To shift distribution use the ``loc`` parameter.
Specifically, ``poisson.pmf(k, mu, loc)`` is identically
equivalent to ``poisson.pmf(k - loc, mu)``.

Examples
--------
>>> import numpy as np
>>> from scipy.stats import poisson
>>> import matplotlib.pyplot as plt
>>> fig, ax = plt.subplots(1, 1)

Calculate the first four moments:

>>> mu = 0.6
>>> mean, var, skew, kurt = poisson.stats(mu, moments='mvsk')

Display the probability mass function (``pmf``):

>>> x = np.arange(poisson.ppf(0.01, mu),
...               poisson.ppf(0.99, mu))
>>> ax.plot(x, poisson.pmf(x, mu), 'bo', ms=8, label='poisson pmf')
>>> ax.vlines(x, 0, poisson.pmf(x, mu), colors='b', lw=5, alpha=0.5)

Alternatively, the distribution object can be called (as a function)
to fix the shape and location. This returns a "frozen" RV object holding
the given parameters fixed.

Freeze the distribution and display the frozen ``pmf``:

>>> rv = poisson(mu)
>>> ax.vlines(x, 0, rv.pmf(x), colors='k', linestyles='-', lw=1,
...         label='frozen pmf')
>>> ax.legend(loc='best', frameon=False)
>>> plt.show()

Check accuracy of ``cdf`` and ``ppf``:

>>> prob = poisson.cdf(x, mu)
>>> np.allclose(x, poisson.ppf(prob, mu))
True

Generate random numbers:

>>> r = poisson.rvs(mu, size=1000)

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