Module « scipy.stats »

Fonction boltzmann - module scipy.stats

Signature de la fonction boltzmann

def boltzmann(*args, **kwds) 

Description

boltzmann.__doc__

A Boltzmann (Truncated Discrete Exponential) random variable.

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

    Notes
    -----
    The probability mass function for `boltzmann` is:

    .. math::

        f(k) = (1-\exp(-\lambda)) \exp(-\lambda k) / (1-\exp(-\lambda N))

    for :math:`k = 0,..., N-1`.

    `boltzmann` takes :math:`\lambda > 0` and :math:`N > 0` as shape parameters.

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

    Examples
    --------
    >>> from scipy.stats import boltzmann
    >>> import matplotlib.pyplot as plt
    >>> fig, ax = plt.subplots(1, 1)
    
    Calculate the first four moments:
    
    >>> lambda_, N = 1.4, 19
    >>> mean, var, skew, kurt = boltzmann.stats(lambda_, N, moments='mvsk')
    
    Display the probability mass function (``pmf``):
    
    >>> x = np.arange(boltzmann.ppf(0.01, lambda_, N),
    ...               boltzmann.ppf(0.99, lambda_, N))
    >>> ax.plot(x, boltzmann.pmf(x, lambda_, N), 'bo', ms=8, label='boltzmann pmf')
    >>> ax.vlines(x, 0, boltzmann.pmf(x, lambda_, N), 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 = boltzmann(lambda_, N)
    >>> 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 = boltzmann.cdf(x, lambda_, N)
    >>> np.allclose(x, boltzmann.ppf(prob, lambda_, N))
    True
    
    Generate random numbers:
    
    >>> r = boltzmann.rvs(lambda_, N, size=1000)