  A non-perturbative random-matrix theory is applied to the transmission of a
monochromatic scalar wave through a disordered waveguide. The probability
distributions of the transmittances T_{mn} and T_n=\sum_m T_{mn} of an incident
mode n are calculated in the thick-waveguide limit, for broken time-reversal
symmetry. A crossover occurs from Rayleigh or Gaussian statistics in the
diffusive regime to lognormal statistics in the localized regime. A
qualitatively different crossover occurs if the disordered region is replaced
by a chaotic cavity. ***Submitted to Physical Review E.***
