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Module « scipy.stats »

Fonction hypergeom - module scipy.stats

Signature de la fonction hypergeom

def hypergeom(*args, **kwds) 

Description

help(scipy.stats.hypergeom)

A hypergeometric discrete random variable.

The hypergeometric distribution models drawing objects from a bin.
`M` is the total number of objects, `n` is total number of Type I objects.
The random variate represents the number of Type I objects in `N` drawn
without replacement from the total population.

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

Notes
-----
The symbols used to denote the shape parameters (`M`, `n`, and `N`) are not
universally accepted.  See the Examples for a clarification of the
definitions used here.

The probability mass function is defined as,

.. math:: p(k, M, n, N) = \frac{\binom{n}{k} \binom{M - n}{N - k}}
                               {\binom{M}{N}}

for :math:`k \in [\max(0, N - M + n), \min(n, N)]`, where the binomial
coefficients are defined as,

.. math:: \binom{n}{k} \equiv \frac{n!}{k! (n - k)!}.

This distribution uses routines from the Boost Math C++ library for
the computation of the ``pmf``, ``cdf``, ``sf`` and ``stats`` methods. [1]_

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

References
----------
.. [1] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.

Examples
--------
>>> import numpy as np
>>> from scipy.stats import hypergeom
>>> import matplotlib.pyplot as plt

Suppose we have a collection of 20 animals, of which 7 are dogs.  Then if
we want to know the probability of finding a given number of dogs if we
choose at random 12 of the 20 animals, we can initialize a frozen
distribution and plot the probability mass function:

>>> [M, n, N] = [20, 7, 12]
>>> rv = hypergeom(M, n, N)
>>> x = np.arange(0, n+1)
>>> pmf_dogs = rv.pmf(x)

>>> fig = plt.figure()
>>> ax = fig.add_subplot(111)
>>> ax.plot(x, pmf_dogs, 'bo')
>>> ax.vlines(x, 0, pmf_dogs, lw=2)
>>> ax.set_xlabel('# of dogs in our group of chosen animals')
>>> ax.set_ylabel('hypergeom PMF')
>>> plt.show()

Instead of using a frozen distribution we can also use `hypergeom`
methods directly.  To for example obtain the cumulative distribution
function, use:

>>> prb = hypergeom.cdf(x, M, n, N)

And to generate random numbers:

>>> R = hypergeom.rvs(M, n, N, size=10)

See Also
--------
nhypergeom, binom, nbinom

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