  For the distinction of the Andreev bound states and Majorana bound states, we
study the waiting time distributions (WTDs) for heterostructures, based on one
dimensional edge states of a two dimensional topological insulators (TI) in
combination with an proximitized s-wave superconductor (SC) and an applied
magnetic field. We show for the time reversal symmetric (TRS) situation of a
Josephson junction details of the WTD. This includes different transport
processes, different numbers of Andreev bound states and the phase difference
of the SC. We further consider a Zeeman field in the normal part of the
junctions revealing novel features in the WTD along the phase transition
between trivial bound states and Majorana bound states. We finally discuss
clear signatures to discriminate between them.
