Module « scipy.stats »

Classe « rv_continuous »

Informations générales

Héritage

builtins.object
    rv_generic
        rv_continuous

Définition

class rv_continuous(rv_generic):

Description _{[extrait de rv_continuous.__doc__]}

A generic continuous random variable class meant for subclassing.

    `rv_continuous` is a base class to construct specific distribution classes
    and instances for continuous random variables. It cannot be used
    directly as a distribution.

    Parameters
    ----------
    momtype : int, optional
        The type of generic moment calculation to use: 0 for pdf, 1 (default)
        for ppf.
    a : float, optional
        Lower bound of the support of the distribution, default is minus
        infinity.
    b : float, optional
        Upper bound of the support of the distribution, default is plus
        infinity.
    xtol : float, optional
        The tolerance for fixed point calculation for generic ppf.
    badvalue : float, optional
        The value in a result arrays that indicates a value that for which
        some argument restriction is violated, default is np.nan.
    name : str, optional
        The name of the instance. This string is used to construct the default
        example for distributions.
    longname : str, optional
        This string is used as part of the first line of the docstring returned
        when a subclass has no docstring of its own. Note: `longname` exists
        for backwards compatibility, do not use for new subclasses.
    shapes : str, optional
        The shape of the distribution. For example ``"m, n"`` for a
        distribution that takes two integers as the two shape arguments for all
        its methods. If not provided, shape parameters will be inferred from
        the signature of the private methods, ``_pdf`` and ``_cdf`` of the
        instance.
    extradoc :  str, optional, deprecated
        This string is used as the last part of the docstring returned when a
        subclass has no docstring of its own. Note: `extradoc` exists for
        backwards compatibility, do not use for new subclasses.
    seed : {None, int, `numpy.random.Generator`,
            `numpy.random.RandomState`}, optional

        If `seed` is None (or `np.random`), the `numpy.random.RandomState`
        singleton is used.
        If `seed` is an int, a new ``RandomState`` instance is used,
        seeded with `seed`.
        If `seed` is already a ``Generator`` or ``RandomState`` instance then
        that instance is used.

    Methods
    -------
    rvs
    pdf
    logpdf
    cdf
    logcdf
    sf
    logsf
    ppf
    isf
    moment
    stats
    entropy
    expect
    median
    mean
    std
    var
    interval
    __call__
    fit
    fit_loc_scale
    nnlf
    support

    Notes
    -----
    Public methods of an instance of a distribution class (e.g., ``pdf``,
    ``cdf``) check their arguments and pass valid arguments to private,
    computational methods (``_pdf``, ``_cdf``). For ``pdf(x)``, ``x`` is valid
    if it is within the support of the distribution.
    Whether a shape parameter is valid is decided by an ``_argcheck`` method
    (which defaults to checking that its arguments are strictly positive.)

    **Subclassing**

    New random variables can be defined by subclassing the `rv_continuous` class
    and re-defining at least the ``_pdf`` or the ``_cdf`` method (normalized
    to location 0 and scale 1).

    If positive argument checking is not correct for your RV
    then you will also need to re-define the ``_argcheck`` method.

    For most of the scipy.stats distributions, the support interval doesn't
    depend on the shape parameters. ``x`` being in the support interval is
    equivalent to ``self.a <= x <= self.b``.  If either of the endpoints of
    the support do depend on the shape parameters, then
    i) the distribution must implement the ``_get_support`` method; and
    ii) those dependent endpoints must be omitted from the distribution's
    call to the ``rv_continuous`` initializer.

    Correct, but potentially slow defaults exist for the remaining
    methods but for speed and/or accuracy you can over-ride::

      _logpdf, _cdf, _logcdf, _ppf, _rvs, _isf, _sf, _logsf

    The default method ``_rvs`` relies on the inverse of the cdf, ``_ppf``,
    applied to a uniform random variate. In order to generate random variates
    efficiently, either the default ``_ppf`` needs to be overwritten (e.g.
    if the inverse cdf can expressed in an explicit form) or a sampling
    method needs to be implemented in a custom ``_rvs`` method.

    If possible, you should override ``_isf``, ``_sf`` or ``_logsf``.
    The main reason would be to improve numerical accuracy: for example,
    the survival function ``_sf`` is computed as ``1 - _cdf`` which can
    result in loss of precision if ``_cdf(x)`` is close to one.

    **Methods that can be overwritten by subclasses**
    ::

      _rvs
      _pdf
      _cdf
      _sf
      _ppf
      _isf
      _stats
      _munp
      _entropy
      _argcheck
      _get_support

    There are additional (internal and private) generic methods that can
    be useful for cross-checking and for debugging, but might work in all
    cases when directly called.

    A note on ``shapes``: subclasses need not specify them explicitly. In this
    case, `shapes` will be automatically deduced from the signatures of the
    overridden methods (`pdf`, `cdf` etc).
    If, for some reason, you prefer to avoid relying on introspection, you can
    specify ``shapes`` explicitly as an argument to the instance constructor.


    **Frozen Distributions**

    Normally, you must provide shape parameters (and, optionally, location and
    scale parameters to each call of a method of a distribution.

    Alternatively, the object may be called (as a function) to fix the shape,
    location, and scale parameters returning a "frozen" continuous RV object:

    rv = generic(<shape(s)>, loc=0, scale=1)
        `rv_frozen` object with the same methods but holding the given shape,
        location, and scale fixed

    **Statistics**

    Statistics are computed using numerical integration by default.
    For speed you can redefine this using ``_stats``:

     - take shape parameters and return mu, mu2, g1, g2
     - If you can't compute one of these, return it as None
     - Can also be defined with a keyword argument ``moments``, which is a
       string composed of "m", "v", "s", and/or "k".
       Only the components appearing in string should be computed and
       returned in the order "m", "v", "s", or "k"  with missing values
       returned as None.

    Alternatively, you can override ``_munp``, which takes ``n`` and shape
    parameters and returns the n-th non-central moment of the distribution.

    Examples
    --------
    To create a new Gaussian distribution, we would do the following:

    >>> from scipy.stats import rv_continuous
    >>> class gaussian_gen(rv_continuous):
    ...     "Gaussian distribution"
    ...     def _pdf(self, x):
    ...         return np.exp(-x**2 / 2.) / np.sqrt(2.0 * np.pi)
    >>> gaussian = gaussian_gen(name='gaussian')

    ``scipy.stats`` distributions are *instances*, so here we subclass
    `rv_continuous` and create an instance. With this, we now have
    a fully functional distribution with all relevant methods automagically
    generated by the framework.

    Note that above we defined a standard normal distribution, with zero mean
    and unit variance. Shifting and scaling of the distribution can be done
    by using ``loc`` and ``scale`` parameters: ``gaussian.pdf(x, loc, scale)``
    essentially computes ``y = (x - loc) / scale`` and
    ``gaussian._pdf(y) / scale``.

    

Constructeur(s)

Signature du constructeur	Description
__init__(self, momtype=1, a=None, b=None, xtol=1e-14, badvalue=None, name=None, longname=None, shapes=None, extradoc=None, seed=None)

Liste des opérateurs

Opérateurs hérités de la classe object

__eq__, __ge__, __gt__, __le__, __lt__, __ne__

Méthodes héritées de la classe rv_generic

__call__, __init_subclass__, __setstate__, __subclasshook__, entropy, freeze, interval, mean, median, moment, rvs, stats, std, support, var

Méthodes héritées de la classe object

__delattr__, __dir__, __format__, __getattribute__, __hash__, __reduce__, __reduce_ex__, __repr__, __setattr__, __sizeof__, __str__