def lorentzian(x, sigma, amp=1, x0=0, const=0):
    """Lorentzian distribution.
    x = independent variable
    sigma = width parameter
    x0 = centre position
    amp = amplitude
    const = y-offset
    """
    return amp * (sigma ** 2 / ((x - x0) ** 2 + sigma ** 2)) + const
