  Using the bosonic numerical renormalization group method, we studied the
equilibrium dynamical correlation function $C(\omega)$ of the spin operator
$\sigma_z$ for the biased sub-Ohmic spin-boson model. The small-$\omega$
behavior $C(\omega) \propto \omega^s$ is found to be universal and independent
of the bias $\epsilon$ and the coupling strength $\alpha$ (except at the
quantum critical point $\alpha =\alpha_c$ and $\epsilon=0$). Our NRG data also
show $C(\omega) \propto \chi^{2}\omega^{s}$ for a wide range of parameters,
including the biased strong coupling regime ($\epsilon \neq 0$ and $\alpha >
\alpha_c$), supporting the general validity of the Shiba relation. Close to the
quantum critical point $\alpha_c$, the dependence of $C(\omega)$ on $\alpha$
and $\epsilon$ is understood in terms of the competition between $\epsilon$ and
the crossover energy scale $\omega_{0}^{\ast}$ of the unbiased case.
$C(\omega)$ is stable with respect to $\epsilon$ for $\epsilon \ll
\epsilon^{\ast}$. For $\epsilon \gg \epsilon^{\ast}$, it is suppressed by
$\epsilon$ in the low frequency regime. We establish that $\epsilon^{\ast}
\propto (\omega_0^{\ast})^{1/\theta}$ holds for all sub-Ohmic regime $0
\leqslant s < 1$, with $\theta=2/(3s)$ for $0 < s \leqslant 1/2$ and $\theta =
2/(1+s)$ for $1/2 < s < 1$. The variation of $C(\omega)$ with $\alpha$ and
$\epsilon$ is summarized into a crossover phase diagram on the
$\alpha-\epsilon$ plane.
