  { In this paper we present a natural and comprehensive generalisation of the
standard factorial moments ($\clFq$) analysis of a multiplicity distribution.
The Generalised Factorial Moments are defined for all $q$ in the complex plane
and, as far as the negative part of its spectrum is concerned, could be useful
for the study of infrared structure of the Strong Interactions Theory of high
energy interactions (LEP multiplicity distribution under the ${\cal Z}_0$). The
QCD calculation of the Generalised Factorial Moments for negative $q$ is
performed in the double leading log accuracy and is compared to OPAL
experimental data. The role played by the infrared cut-off of the model is
discussed and illustrated with a Monte Carlo calculation. }

High Energy Physics - Phenomenology