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Module « scipy.stats »

Fonction f - module scipy.stats

Signature de la fonction f

def f(*args, **kwds) 

Description

help(scipy.stats.f)

An F continuous random variable.

For the noncentral F distribution, see `ncf`.

As an instance of the `rv_continuous` class, `f` 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(dfn, dfd, loc=0, scale=1, size=1, random_state=None)
    Random variates.
pdf(x, dfn, dfd, loc=0, scale=1)
    Probability density function.
logpdf(x, dfn, dfd, loc=0, scale=1)
    Log of the probability density function.
cdf(x, dfn, dfd, loc=0, scale=1)
    Cumulative distribution function.
logcdf(x, dfn, dfd, loc=0, scale=1)
    Log of the cumulative distribution function.
sf(x, dfn, dfd, loc=0, scale=1)
    Survival function  (also defined as ``1 - cdf``, but `sf` is sometimes more accurate).
logsf(x, dfn, dfd, loc=0, scale=1)
    Log of the survival function.
ppf(q, dfn, dfd, loc=0, scale=1)
    Percent point function (inverse of ``cdf`` --- percentiles).
isf(q, dfn, dfd, loc=0, scale=1)
    Inverse survival function (inverse of ``sf``).
moment(order, dfn, dfd, loc=0, scale=1)
    Non-central moment of the specified order.
stats(dfn, dfd, loc=0, scale=1, moments='mv')
    Mean('m'), variance('v'), skew('s'), and/or kurtosis('k').
entropy(dfn, dfd, loc=0, scale=1)
    (Differential) entropy of the RV.
fit(data)
    Parameter estimates for generic data.
    See `scipy.stats.rv_continuous.fit <https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.rv_continuous.fit.html#scipy.stats.rv_continuous.fit>`__ for detailed documentation of the
    keyword arguments.
expect(func, args=(dfn, dfd), loc=0, scale=1, lb=None, ub=None, conditional=False, **kwds)
    Expected value of a function (of one argument) with respect to the distribution.
median(dfn, dfd, loc=0, scale=1)
    Median of the distribution.
mean(dfn, dfd, loc=0, scale=1)
    Mean of the distribution.
var(dfn, dfd, loc=0, scale=1)
    Variance of the distribution.
std(dfn, dfd, loc=0, scale=1)
    Standard deviation of the distribution.
interval(confidence, dfn, dfd, loc=0, scale=1)
    Confidence interval with equal areas around the median.

See Also
--------
ncf

Notes
-----
The F distribution with :math:`df_1 > 0` and :math:`df_2 > 0` degrees of freedom is
the distribution of the ratio of two independent chi-squared distributions with
:math:`df_1` and :math:`df_2` degrees of freedom, after rescaling by
:math:`df_2 / df_1`.

The probability density function for `f` is:

.. math::

    f(x, df_1, df_2) = \frac{df_2^{df_2/2} df_1^{df_1/2} x^{df_1 / 2-1}}
                            {(df_2+df_1 x)^{(df_1+df_2)/2}
                             B(df_1/2, df_2/2)}

for :math:`x > 0`.

`f` accepts shape parameters ``dfn`` and ``dfd`` for :math:`df_1`, the degrees of
freedom of the chi-squared distribution in the numerator, and :math:`df_2`, the
degrees of freedom of the chi-squared distribution in the denominator, respectively.

The probability density above is defined in the "standardized" form. To shift
and/or scale the distribution use the ``loc`` and ``scale`` parameters.
Specifically, ``f.pdf(x, dfn, dfd, loc, scale)`` is identically
equivalent to ``f.pdf(y, dfn, dfd) / scale`` with
``y = (x - loc) / scale``. Note that shifting the location of a distribution
does not make it a "noncentral" distribution; noncentral generalizations of
some distributions are available in separate classes.

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

Calculate the first four moments:

>>> dfn, dfd = 29, 18
>>> mean, var, skew, kurt = f.stats(dfn, dfd, moments='mvsk')

Display the probability density function (``pdf``):

>>> x = np.linspace(f.ppf(0.01, dfn, dfd),
...                 f.ppf(0.99, dfn, dfd), 100)
>>> ax.plot(x, f.pdf(x, dfn, dfd),
...        'r-', lw=5, alpha=0.6, label='f pdf')

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

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

>>> rv = f(dfn, dfd)
>>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')

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

>>> vals = f.ppf([0.001, 0.5, 0.999], dfn, dfd)
>>> np.allclose([0.001, 0.5, 0.999], f.cdf(vals, dfn, dfd))
True

Generate random numbers:

>>> r = f.rvs(dfn, dfd, size=1000)

And compare the histogram:

>>> ax.hist(r, density=True, bins='auto', histtype='stepfilled', alpha=0.2)
>>> ax.set_xlim([x[0], x[-1]])
>>> ax.legend(loc='best', frameon=False)
>>> plt.show()

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