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Module « scipy.stats »

Fonction bernoulli - module scipy.stats

Signature de la fonction bernoulli

def bernoulli(*args, **kwds) 

Description

help(scipy.stats.bernoulli)

A Bernoulli discrete random variable.

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

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

.. math::

   f(k) = \begin{cases}1-p  &\text{if } k = 0\\
                       p    &\text{if } k = 1\end{cases}

for :math:`k` in :math:`\{0, 1\}`, :math:`0 \leq p \leq 1`

`bernoulli` takes :math:`p` as shape parameter,
where :math:`p` is the probability of a single success
and :math:`1-p` is the probability of a single failure.

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

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

Calculate the first four moments:

>>> p = 0.3
>>> mean, var, skew, kurt = bernoulli.stats(p, moments='mvsk')

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

>>> x = np.arange(bernoulli.ppf(0.01, p),
...               bernoulli.ppf(0.99, p))
>>> ax.plot(x, bernoulli.pmf(x, p), 'bo', ms=8, label='bernoulli pmf')
>>> ax.vlines(x, 0, bernoulli.pmf(x, p), 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 = bernoulli(p)
>>> 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 = bernoulli.cdf(x, p)
>>> np.allclose(x, bernoulli.ppf(prob, p))
True

Generate random numbers:

>>> r = bernoulli.rvs(p, size=1000)

Vous êtes un professionnel et vous avez besoin d'une formation ? Programmation Python
Les fondamentaux Voir le programme détaillé