  We investigate the superfluid-insulator quantum phase transition in a
disordered 1D Bose gas in the mean field limit, by studying the probability
distribution of the density. The superfluid phase is characterized by a
vanishing probability to have zero density, whereas a nonzero probability marks
the insulator phase. This relation is derived analytically, and confirmed by a
numerical study. This fragmentation criterion is particularly suited for
detecting the phase transition in experiments. When a harmonic trap is
included, the transition to the insulating phase can be extracted from the
statistics of the local density distribution.
