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Fonction exponnorm - module scipy.stats

Signature de la fonction exponnorm

def exponnorm(*args, **kwds) 

Description

exponnorm.__doc__

An exponentially modified Normal continuous random variable.

    Also known as the exponentially modified Gaussian distribution [1]_.

    As an instance of the `rv_continuous` class, `exponnorm` 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(K, loc=0, scale=1, size=1, random_state=None)
        Random variates.
    pdf(x, K, loc=0, scale=1)
        Probability density function.
    logpdf(x, K, loc=0, scale=1)
        Log of the probability density function.
    cdf(x, K, loc=0, scale=1)
        Cumulative distribution function.
    logcdf(x, K, loc=0, scale=1)
        Log of the cumulative distribution function.
    sf(x, K, loc=0, scale=1)
        Survival function  (also defined as ``1 - cdf``, but `sf` is sometimes more accurate).
    logsf(x, K, loc=0, scale=1)
        Log of the survival function.
    ppf(q, K, loc=0, scale=1)
        Percent point function (inverse of ``cdf`` --- percentiles).
    isf(q, K, loc=0, scale=1)
        Inverse survival function (inverse of ``sf``).
    moment(n, K, loc=0, scale=1)
        Non-central moment of order n
    stats(K, loc=0, scale=1, moments='mv')
        Mean('m'), variance('v'), skew('s'), and/or kurtosis('k').
    entropy(K, 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=(K,), 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(K, loc=0, scale=1)
        Median of the distribution.
    mean(K, loc=0, scale=1)
        Mean of the distribution.
    var(K, loc=0, scale=1)
        Variance of the distribution.
    std(K, loc=0, scale=1)
        Standard deviation of the distribution.
    interval(alpha, K, loc=0, scale=1)
        Endpoints of the range that contains fraction alpha [0, 1] of the
        distribution

    Notes
    -----
    The probability density function for `exponnorm` is:

    .. math::

        f(x, K) = \frac{1}{2K} \exp\left(\frac{1}{2 K^2} - x / K \right)
                  \text{erfc}\left(-\frac{x - 1/K}{\sqrt{2}}\right)

    where :math:`x` is a real number and :math:`K > 0`.

    It can be thought of as the sum of a standard normal random variable
    and an independent exponentially distributed random variable with rate
    ``1/K``.

    The probability density above is defined in the "standardized" form. To shift
    and/or scale the distribution use the ``loc`` and ``scale`` parameters.
    Specifically, ``exponnorm.pdf(x, K, loc, scale)`` is identically
    equivalent to ``exponnorm.pdf(y, K) / 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.

    An alternative parameterization of this distribution (for example, in
    the Wikpedia article [1]_) involves three parameters, :math:`\mu`,
    :math:`\lambda` and :math:`\sigma`.

    In the present parameterization this corresponds to having ``loc`` and
    ``scale`` equal to :math:`\mu` and :math:`\sigma`, respectively, and
    shape parameter :math:`K = 1/(\sigma\lambda)`.

    .. versionadded:: 0.16.0

    References
    ----------
    .. [1] Exponentially modified Gaussian distribution, Wikipedia,
           https://en.wikipedia.org/wiki/Exponentially_modified_Gaussian_distribution

    Examples
    --------
    >>> from scipy.stats import exponnorm
    >>> import matplotlib.pyplot as plt
    >>> fig, ax = plt.subplots(1, 1)
    
    Calculate the first four moments:
    
    >>> K = 1.5
    >>> mean, var, skew, kurt = exponnorm.stats(K, moments='mvsk')
    
    Display the probability density function (``pdf``):
    
    >>> x = np.linspace(exponnorm.ppf(0.01, K),
    ...                 exponnorm.ppf(0.99, K), 100)
    >>> ax.plot(x, exponnorm.pdf(x, K),
    ...        'r-', lw=5, alpha=0.6, label='exponnorm 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 = exponnorm(K)
    >>> ax.plot(x, rv.pdf(x), 'k-', lw=2, label='frozen pdf')
    
    Check accuracy of ``cdf`` and ``ppf``:
    
    >>> vals = exponnorm.ppf([0.001, 0.5, 0.999], K)
    >>> np.allclose([0.001, 0.5, 0.999], exponnorm.cdf(vals, K))
    True
    
    Generate random numbers:
    
    >>> r = exponnorm.rvs(K, size=1000)
    
    And compare the histogram:
    
    >>> ax.hist(r, density=True, histtype='stepfilled', alpha=0.2)
    >>> ax.legend(loc='best', frameon=False)
    >>> plt.show()