  Various parametrizations of the multiplicity distribution are studied using
the recently published large statistics OPAL results on multidimensional local
fluctuations and genuine correlations in e+e- -> Z -> hadrons. The measured
normalized factorial and cumulant moments are compared to the predictions of
the negative binomial distribution, the modified and generalized versions of
it, the log-normal distribution and the model of the generalized birth process
with immigration. This is the first study which uses the multiplicity
distribution parametrizations to describe high-order genuine correlations.
Although the parametrizations fit well the measured fluctuations and
correlations for low orders, they do show certain deviations at high orders. We
have shown that it is necessary to incorporate the multiparticle character of
the correlations along with the property of self-similarity to attain a good
description of the measurements.
