  Up to now several gravitational-wave events from the coalescences of black
hole binaries have been reported by LIGO/VIRGO, and imply that black holes
should have an extended mass function. We work out the merger rate distribution
of primordial-black-hole binaries with a general mass function by taking into
account the torques by all primordial black holes and linear density
perturbations. In the future, many more coalescences of black hole binaries are
expected to be detected, and the one-dimensional and two-dimensional merger
rate distributions will be crucial for reconstructing the mass function of
primordial black holes.
