  We consider random quantum (tight-binding, XX and Ising) spin chains in the
off-critical region and study their Griffiths-McCoy singularities. These are
obtained from the density of states of the low-energy excitations, which is
calculated exactly by the Dyson-Schmidt method. In large finite systems the
low-energy excitations are shown to follow the statistics of extremes and their
distribution is given by the Fr\'echet form. Relation between the Dyson-Schmidt
technique and the strong disorder renormalization group method is also
discussed.
