def centralmoment(vi, k):
    """
    Converts raw distribution moments to central moments
    
    Parameters
    ----------
    vi : array
        The first four raw distribution moments
    k : int
        The central moment (0 to 4) to calculate (i.e., k=2 is the variance)
    
    Returns
    -------
    cm : scalar
        The central moment itself
        
    """
    if k == 0:
        ans = 1
    elif k == 1:
        ans = 0
    elif k == 2:
        ans = vi[2] - vi[1] ** 2
    elif k == 3:
        ans = vi[3] - 3 * vi[2] * vi[1] + 2 * vi[1] ** 3
    elif k == 4:
        ans = vi[4] - 4 * vi[3] * vi[1] + 6 * vi[2] * vi[1] ** 2 - 3 * vi[1
            ] ** 4
    else:
        print('Can only calculate central moments k = 0 to 4. Sorry.')
        ans = None
    return ans
