  Shot noise and higher current moments T_M=<Tr (t^+t)^M> are studied within
the Anderson model of disordered conductors in dimensions d= 2, 3 and 4. Here t
denotes a transmission matrix. We calculate the conductance G=T_1, shot noise
S=T_1-T_2, Fano factor F=S/G and ratios C_M=T_M/G, and we show indications that
all of them are as good order parameters as the conductance itself. In the
limit of infinite system size, two limiting values of F and C_M are found; the
stable one in the metallic regime, and the unstable one, characterizing the
critical point for d > 2. We present analytical expressions for both limiting
values, together with a compact formula for current cumulants at 3D
criticality. Our data confirm also Nazarov's microscopic theory [PRB 52, 4720
(1995)], as we show numerically for special linear combinations of T_M.
