  Oscillations in modified combinants ($C_j$s) have been of interest to
multiparticle production mechanisms since the 1990s. Recently, there has been a
discussion on how these oscillations can be reproduced by compounding a
binomial distribution with a negative binomial distribution. In this work, we
explore a stochastic branching model based on a simple interaction term
$\lambda\overline{\psi}\phi\psi$ for partons and propose a hadronization scheme
to arrive at the final multiplicity distribution. We study the effects that
compounding our model with a binomial distribution has on $C_j$s and explore
its physical implications. We find that there is a significant difference in
the oscillations in $C_j$s between high energy $pp$ and $p\bar{p}$ scattering
that our model can reproduce.
