Factorial moments of continuous order

The normalized factorial moments ${\mathit{F}}_{\mathit{q}}$ are continued to noninteger values of the order q, satisfying the condition that the statistical fluctuations remain filtered out. That is, for the Poisson distribution ${\mathit{F}}_{\mathit{q}}$=1 for all q. The continuation procedure is deisgned with phenomenology and data analysis in mind. Examples are given to show how ${\mathit{F}}_{\mathit{q}}$ can be obtained for positive and negative values of q. With q being continuous, a multifractal analysis is made possible for multiplicity distributions that arise from self-similar dynamics. A step-by-step procedure of the method is summarized in the conclusion.