  The spin-boson model has nontrivial quantum phase transitions in the
sub-Ohmic regime. For the bath spectra exponent $0 \leqslant s<1/2$, the
bosonic numerical renormalization group (BNRG) study of the exponents $\beta$
and $\delta$ are hampered by the boson state truncation which leads to
artificial interacting exponents instead of the correct Gaussian ones. In this
paper, guided by a mean-field calculation, we study the order parameter
function $m(\tau=\alpha-\alpha_c, \epsilon, \Delta)$ using BNRG. Scaling
analysis with respect to the boson state truncation $N_{b}$, the logarithmic
discretization parameter $\Lambda$, and the tunneling strength $\Delta$ are
carried out. Truncation-induced multiple-power behaviors are observed close to
the critical point, with artificial values of $\beta$ and $\delta$. They cross
over to classical behaviors with exponents $\beta=1/2$ and $\delta=3$ on the
intermediate scales of $\tau$ and $\epsilon$, respectively. We also find
$\tau/\Delta^{1-s}$ and $\epsilon/\Delta$ scalings in the function $m(\tau,
\epsilon, \Delta)$. The role of boson state truncation as a scaling variable in
the BNRG result for $0 \leqslant s<1/2$ is identified and its interplay with
the logarithmic discretization revealed. Relevance to the validity of
quantum-to-classical mapping in other impurity models is discussed.
