Multiplicity distributions of negative binomial distribution (NBD) and modi
fied NBD are obtained from it birth process model with an immigration. The
ratio of factorial cumulant moment to factorial moment, i.e., H moment is c
alculated from different multiplicity distributions of NBD, modified NBD an
d the three fireball model, which shows an oscillatory behavior when there
is a truncation of multiplicity. The oscillation of H moment is related to
the common character of the truncated multiplicity distributions.