Module « scipy.stats »

Fonction skellam - module scipy.stats

Signature de la fonction skellam

def skellam(*args, **kwds) 

Description

skellam.__doc__

A  Skellam discrete random variable.

    As an instance of the `rv_discrete` class, `skellam` 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(mu1, mu2, loc=0, size=1, random_state=None)
        Random variates.
    pmf(k, mu1, mu2, loc=0)
        Probability mass function.
    logpmf(k, mu1, mu2, loc=0)
        Log of the probability mass function.
    cdf(k, mu1, mu2, loc=0)
        Cumulative distribution function.
    logcdf(k, mu1, mu2, loc=0)
        Log of the cumulative distribution function.
    sf(k, mu1, mu2, loc=0)
        Survival function  (also defined as ``1 - cdf``, but `sf` is sometimes more accurate).
    logsf(k, mu1, mu2, loc=0)
        Log of the survival function.
    ppf(q, mu1, mu2, loc=0)
        Percent point function (inverse of ``cdf`` --- percentiles).
    isf(q, mu1, mu2, loc=0)
        Inverse survival function (inverse of ``sf``).
    stats(mu1, mu2, loc=0, moments='mv')
        Mean('m'), variance('v'), skew('s'), and/or kurtosis('k').
    entropy(mu1, mu2, loc=0)
        (Differential) entropy of the RV.
    expect(func, args=(mu1, mu2), loc=0, lb=None, ub=None, conditional=False)
        Expected value of a function (of one argument) with respect to the distribution.
    median(mu1, mu2, loc=0)
        Median of the distribution.
    mean(mu1, mu2, loc=0)
        Mean of the distribution.
    var(mu1, mu2, loc=0)
        Variance of the distribution.
    std(mu1, mu2, loc=0)
        Standard deviation of the distribution.
    interval(alpha, mu1, mu2, loc=0)
        Endpoints of the range that contains fraction alpha [0, 1] of the
        distribution

    Notes
    -----
    Probability distribution of the difference of two correlated or
    uncorrelated Poisson random variables.

    Let :math:`k_1` and :math:`k_2` be two Poisson-distributed r.v. with
    expected values :math:`\lambda_1` and :math:`\lambda_2`. Then,
    :math:`k_1 - k_2` follows a Skellam distribution with parameters
    :math:`\mu_1 = \lambda_1 - \rho \sqrt{\lambda_1 \lambda_2}` and
    :math:`\mu_2 = \lambda_2 - \rho \sqrt{\lambda_1 \lambda_2}`, where
    :math:`\rho` is the correlation coefficient between :math:`k_1` and
    :math:`k_2`. If the two Poisson-distributed r.v. are independent then
    :math:`\rho = 0`.

    Parameters :math:`\mu_1` and :math:`\mu_2` must be strictly positive.

    For details see: https://en.wikipedia.org/wiki/Skellam_distribution

    `skellam` takes :math:`\mu_1` and :math:`\mu_2` as shape parameters.

    The probability mass function above is defined in the "standardized" form.
    To shift distribution use the ``loc`` parameter.
    Specifically, ``skellam.pmf(k, mu1, mu2, loc)`` is identically
    equivalent to ``skellam.pmf(k - loc, mu1, mu2)``.

    Examples
    --------
    >>> from scipy.stats import skellam
    >>> import matplotlib.pyplot as plt
    >>> fig, ax = plt.subplots(1, 1)
    
    Calculate the first four moments:
    
    >>> mu1, mu2 = 15, 8
    >>> mean, var, skew, kurt = skellam.stats(mu1, mu2, moments='mvsk')
    
    Display the probability mass function (``pmf``):
    
    >>> x = np.arange(skellam.ppf(0.01, mu1, mu2),
    ...               skellam.ppf(0.99, mu1, mu2))
    >>> ax.plot(x, skellam.pmf(x, mu1, mu2), 'bo', ms=8, label='skellam pmf')
    >>> ax.vlines(x, 0, skellam.pmf(x, mu1, mu2), 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 = skellam(mu1, mu2)
    >>> 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 = skellam.cdf(x, mu1, mu2)
    >>> np.allclose(x, skellam.ppf(prob, mu1, mu2))
    True
    
    Generate random numbers:
    
    >>> r = skellam.rvs(mu1, mu2, size=1000)