  Various phenomenological models of particle multiplicity distributions are
discussed using a general form of a unified model which is based on the grand
canonical partition function and Feynman's path integral approach to
statistical processes. These models can be written as special cases of a more
general distribution which has three control parameters which are $a$, $x$,
$z$. The relation to these parameters to various physical quantities are
discussed. A connection of the parameter $a$ with Fisher's critical exponent
$\tau$ is developed. Using this grand canonical approach, moments, cumulants
and combinants are discussed and a physical interpretation of the combinants
are given and their behavior connected to the critical exponent $\tau$. Various
physical phenomena such as hierarchical structure, void scaling relations, KNO
scaling features, clan variables, and branching laws are shown in terms of this
general approach. Several of these features which were previously developed in
terms of the negative binomial distribution are found to be more general. Both
hierarchical structure and void scaling relations depend on the Fisher exponent
$\tau$. Applications of our approach to the charged particle multiplicity
distribution in jets of L3 and H1 data are given. It is shown that just looking
at the mean and fluctuation of data is not enough to distinguish these
distributions or the underlying mechanism. The mean, fluctuation and third
cummulant of distribution determine three parameters $x$, $z$, $a$. We find
that a generalized random work model fits the data better than the widely used
negative binomial model.
