Factorial moments of continuous order.

The normalized factorial moments Fq are continued to noninteger values of the order q, satisfying the condition that the statistical fluctuations remain filtered out. That is, for Poisson distribution Fq = 1 for all q. The continuation procedure is designed with phenomenology and data analysis in mind. Examples are given to show how Fq can be obtained for positive and negative values of q. With q being continuous, 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.