Factorial Moments of Continuous Order

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