The problem of eliminating the statistical fluctuations and extracting the event dynamics from event-by-event analysis is discussed. New moments $G_p$ (for continuous distribution), and $G_{q,p}$ (for anomalous distribution) are proposed, which are experimentally measurable and can eliminate the Poissonian type statistical fluctuations to recover the dynamical moments $C_p$ and $C_{q,p}$. In this way, the dynamical distribution of the event-averaged transverse momentum $\bar{\pt}$ can be extracted, and the anomalous scaling of dynamical distribution, if exists, can be recovered, through event-by-event analysis of experimental data.

15 pages, 2 eps figures, Phys. Rev. C accepted