  Based on a local mean-field theory approach at Anderson localization, we find
a distribution function of critical temperature from that of disorder. An
essential point of this local mean-field theory approach is that the
information of the wave-function multifractality is introduced. The
distribution function of the Kondo temperature ($T_{K}$) shows a power-law tail
in the limit of $T_{K} \rightarrow 0$ regardless of the Kondo coupling
constant. We also find that the distribution function of the ferromagnetic
transition temperature ($T_{c}$) gives a power-law behavior in the limit of
$T_{c} \rightarrow 0$ when an interaction parameter for ferromagnetic
instability lies below a critical value. However, the $T_{c}$ distribution
function stops the power-law increasing behavior in the $T_{c} \rightarrow 0$
limit and vanishes beyond the critical interaction parameter inside the
ferromagnetic phase. These results imply that the typical Kondo temperature
given by a geometric average always vanishes due to finite density of the
distribution function in the $T_{K} \rightarrow 0$ limit while the typical
ferromagnetic transition temperature shows a phase transition at the critical
interaction parameter. We propose that the typical transition temperature
serves a criterion for quantum Griffiths phenomena vs. smeared transitions:
Quantum Griffiths phenomena occur above the typical value of the critical
temperature while smeared phase transitions result at low temperatures below
the typical transition temperature. We speculate that the ferromagnetic
transition at Anderson localization shows the evolution from quantum Griffiths
phenomena to smeared transitions around the critical interaction parameter at
low temperatures.
