  We study the statistical properties of the off-diagonal matrix elements of
observables in the energy eigenstates of integrable quantum systems. They have
been found to be dense in the spin-1/2 XXZ chain, while they are sparse in
noninteracting systems. We focus on the quasimomentum occupation of hard-core
bosons in one dimension, and show that the distributions of the off-diagonal
matrix elements are well described by generalized Gamma distributions, in both
the presence and absence of translational invariance but not in the presence of
localization. We also show that the results obtained for the off-diagonal
matrix elements of observables in the spin-1/2 XXZ model are well described by
a generalized Gamma distribution.
