def FPE(N, rho, k=None):
    """Final prediction error criterion

    .. math:: FPE(k) = \\frac{N + k + 1}{N - k - 1} \\rho_k

    :validation: double checked versus octave.

    """
    fpe = rho * (N + k + 1.0) / (N - k - 1)
    return fpe
