def tau_davies(Z, fmax, t, y, dy, normalization='standard', dH=1, dK=3):
    """tau factor for estimating Davies bound (Baluev 2008, Table 1)"""
    N = len(t)
    NH = N - dH  # DOF for null hypothesis
    NK = N - dK  # DOF for periodic hypothesis
    Dt = _weighted_var(t, dy)
    Teff = np.sqrt(4 * np.pi * Dt)
    W = fmax * Teff
    if normalization == 'psd':
        # 'psd' normalization is same as Baluev's z
        return W * np.exp(-Z) * np.sqrt(Z)
    elif normalization == 'standard':
        # 'standard' normalization is Z = 2/NH * z_1
        return (_gamma(NH) * W * (1 - Z) ** (0.5 * (NK - 1))
                * np.sqrt(0.5 * NH * Z))
    elif normalization == 'model':
        # 'model' normalization is Z = 2/NK * z_2
        return (_gamma(NK) * W * (1 + Z) ** (-0.5 * NK)
                * np.sqrt(0.5 * NK * Z))
    elif normalization == 'log':
        # 'log' normalization is Z = 2/NK * z_3
        return (_gamma(NK) * W * np.exp(-0.5 * Z * (NK - 0.5))
                * np.sqrt(NK * np.sinh(0.5 * Z)))
    else:
        raise NotImplementedError("normalization={0}".format(normalization))