  A three-parameter discrete distribution is developed to describe the
multiplicity distributions observed in total- and limited phase space volumes
in different collision processes. The probability law is obtained by the
Poisson transform of the KNO scaling function derived in Polyakov's similarity
hypothesis for strong interactions as well as in perturbative QCD. Various
characteristics of the newly proposed distribution are investigated e.g. its
generating function, factorial moments, factorial cumulants. Several limiting
and special cases are discussed. A comparison is made to the multiplicity data
available in e+e- annihilations at the Z0 peak.
