def lorentz1D(x, x0, w):
    """Returns the probability density function of the Lorentzian (aka Cauchy) function with maximum at 1.

    Parameters
    ----------
        x: ndarray or list
            A 1D vector of points for the dependent variable
        x0: float
            The center of the peak maximum
        w: float
            The parameter that modifies the width of the distribution.

    Returns
    -------
        l: ndarray
            A vector of size (N,) of the Lorentzian distribution evaluated
            at the input x values.

    """
    return w ** 2 / ((x - x0) ** 2 + w ** 2)