Classe « rv_continuous »

Méthode scipy.stats.rv_continuous.expect

Signature de la méthode expect

def expect(self, func=None, args=(), loc=0, scale=1, lb=None, ub=None, conditional=False, **kwds) 

Description

expect.__doc__

Calculate expected value of a function with respect to the
        distribution by numerical integration.

        The expected value of a function ``f(x)`` with respect to a
        distribution ``dist`` is defined as::

                    ub
            E[f(x)] = Integral(f(x) * dist.pdf(x)),
                    lb

        where ``ub`` and ``lb`` are arguments and ``x`` has the ``dist.pdf(x)``
        distribution. If the bounds ``lb`` and ``ub`` correspond to the
        support of the distribution, e.g. ``[-inf, inf]`` in the default
        case, then the integral is the unrestricted expectation of ``f(x)``.
        Also, the function ``f(x)`` may be defined such that ``f(x)`` is ``0``
        outside a finite interval in which case the expectation is
        calculated within the finite range ``[lb, ub]``.

        Parameters
        ----------
        func : callable, optional
            Function for which integral is calculated. Takes only one argument.
            The default is the identity mapping f(x) = x.
        args : tuple, optional
            Shape parameters of the distribution.
        loc : float, optional
            Location parameter (default=0).
        scale : float, optional
            Scale parameter (default=1).
        lb, ub : scalar, optional
            Lower and upper bound for integration. Default is set to the
            support of the distribution.
        conditional : bool, optional
            If True, the integral is corrected by the conditional probability
            of the integration interval.  The return value is the expectation
            of the function, conditional on being in the given interval.
            Default is False.

        Additional keyword arguments are passed to the integration routine.

        Returns
        -------
        expect : float
            The calculated expected value.

        Notes
        -----
        The integration behavior of this function is inherited from
        `scipy.integrate.quad`. Neither this function nor
        `scipy.integrate.quad` can verify whether the integral exists or is
        finite. For example ``cauchy(0).mean()`` returns ``np.nan`` and
        ``cauchy(0).expect()`` returns ``0.0``.

        The function is not vectorized.

        Examples
        --------

        To understand the effect of the bounds of integration consider

        >>> from scipy.stats import expon
        >>> expon(1).expect(lambda x: 1, lb=0.0, ub=2.0)
        0.6321205588285578

        This is close to

        >>> expon(1).cdf(2.0) - expon(1).cdf(0.0)
        0.6321205588285577

        If ``conditional=True``

        >>> expon(1).expect(lambda x: 1, lb=0.0, ub=2.0, conditional=True)
        1.0000000000000002

        The slight deviation from 1 is due to numerical integration.