  This paper proves that if a discrete distribution is infinitely divisible
(ID) with integer-valued components, then it has a mass at the origin, which
also implies why certain ID discrete laws do not have gaps in its support. We
argue that discrete laws also can be stable and such laws do have domain of
attraction. Then we give certain recent developments and references not
reported in the Bose Dasgupta Rubin (2002) review in Sankhya, and some examples
in the topics; infinite divisibility and stability of discrete laws, random
infinite divisibility, operator stable laws, class-L laws, Goldie-Steutel
result, max-infinite divisibility and stability, simulation, alternate stable
laws, applications and free probability theory.
